Menu Close

How-many-different-words-of-4-letters-can-be-formed-from-the-word-Flat-earth-

Tinku Tara 0 Comments
Pin




Question Number 178219 by Acem last updated on 14/Oct/22
How many different words of 4 letters can be formed from the word Flat earth
$${How}\:{many}\:{different}\:{words}\:{of}\:\mathrm{4}\:{letters}\:{can} \\ $$$$\:{be}\:{formed}\:{from}\:{the}\:{word}\:\boldsymbol{{Flat}}\:\boldsymbol{{earth}} \\ $$$$ \\ $$
Commented by Acem last updated on 14/Oct/22
I sweep it over the planet
$$\:{I}\:{sweep}\:{it}\:{over}\:{the}\:{planet} \\ $$
Commented by Observer last updated on 14/Oct/22
Are you a flat earther?
$${Are}\:{you}\:{a}\:{flat}\:{earther}? \\ $$
Answered by JDamian last updated on 14/Oct/22
I see you need much help in Maths as you cannot find two words in Flat earth.
$${I}\:{see}\:{you}\:{need}\:{much}\:{help}\:{in}\:{Maths}\:{as}\:{you} \\ $$$${cannot}\:{find}\:\boldsymbol{{two}}\:{words}\:{in}\:{Flat}\:{earth}. \\ $$
Answered by mr W last updated on 14/Oct/22
number of 4 letter words formed from the letters flat earth 1) 4 different letters words like xyzw with x,y,z,w choosen from (f,l,a,t,e,r,h). to select 4 letters, there are C_4 ^7 ways. with 4 letters we can form 4! words. therefore we can get C_4 ^7 ×4!=840 words. 2) two letters a words like aaxy with x,y choosen from (f,l,t,e,r,h). to select 2 letters, there are C_2 ^6 ways. with 4 letters we can form ((4!)/(2!)) words. therefore we can get C_2 ^6 ×((4!)/(2!))=180 words. 3) two letters t words like ttxy. similarly we can get C_2 ^6 ×((4!)/(2!))=180 words. 4) two letters a and two letters t words like aatt. we can get ((4!)/(2!2!))=6 words. totally: 840+2×180+6=1206 words
$${number}\:{of}\:\mathrm{4}\:{letter}\:{words}\:{formed}\: \\ $$$${from}\:{the}\:{letters}\:{flat}\:{earth} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{4}\:{different}\:{letters} \\ $$$${words}\:{like}\:{xyzw}\:{with}\:{x},{y},{z},{w}\:{choosen} \\ $$$${from}\:\left({f},{l},{a},{t},{e},{r},{h}\right).\:{to}\:{select}\:\mathrm{4}\:{letters}, \\ $$$${there}\:{are}\:{C}_{\mathrm{4}} ^{\mathrm{7}} \:{ways}.\:{with}\:\mathrm{4}\:{letters}\:{we}\:{can} \\ $$$${form}\:\mathrm{4}!\:{words}.\:{therefore}\:{we}\:{can}\:{get} \\ $$$${C}_{\mathrm{4}} ^{\mathrm{7}} ×\mathrm{4}!=\mathrm{840}\:{words}. \\ $$$$\left.\mathrm{2}\right)\:{two}\:{letters}\:{a} \\ $$$${words}\:{like}\:{aaxy}\:{with}\:{x},{y}\:{choosen} \\ $$$${from}\:\left({f},{l},{t},{e},{r},{h}\right).\:{to}\:{select}\:\mathrm{2}\:{letters}, \\ $$$${there}\:{are}\:{C}_{\mathrm{2}} ^{\mathrm{6}} \:{ways}.\:{with}\:\mathrm{4}\:{letters}\:{we}\: \\ $$$${can}\:{form}\:\frac{\mathrm{4}!}{\mathrm{2}!}\:{words}.\:{therefore}\:{we}\:{can}\: \\ $$$${get}\:{C}_{\mathrm{2}} ^{\mathrm{6}} ×\frac{\mathrm{4}!}{\mathrm{2}!}=\mathrm{180}\:{words}. \\ $$$$\left.\mathrm{3}\right)\:{two}\:{letters}\:{t} \\ $$$${words}\:{like}\:{ttxy}. \\ $$$${similarly}\:{we}\:{can}\:{get} \\ $$$${C}_{\mathrm{2}} ^{\mathrm{6}} ×\frac{\mathrm{4}!}{\mathrm{2}!}=\mathrm{180}\:{words}. \\ $$$$\left.\mathrm{4}\right)\:{two}\:{letters}\:{a}\:{and}\:{two}\:{letters}\:{t} \\ $$$${words}\:{like}\:{aatt}.\:{we}\:{can}\:{get} \\ $$$$\frac{\mathrm{4}!}{\mathrm{2}!\mathrm{2}!}=\mathrm{6}\:{words}. \\ $$$$ \\ $$$${totally}:\:\mathrm{840}+\mathrm{2}×\mathrm{180}+\mathrm{6}=\mathrm{1206}\:{words} \\ $$
Commented by mr W last updated on 14/Oct/22
using the 5 letters SYRIA you can only form 5×4×3=60 words with 3 letters! words like SSR or SSS are not valid, because you have only one letter S.
$${using}\:{the}\:\mathrm{5}\:{letters}\:{SYRIA}\:{you}\:{can}\:{only} \\ $$$${form}\:\mathrm{5}×\mathrm{4}×\mathrm{3}=\mathrm{60}\:{words}\:{with}\:\mathrm{3}\:{letters}! \\ $$$${words}\:{like}\:{SSR}\:{or}\:{SSS}\:{are}\:{not}\:{valid},\: \\ $$$${because}\:{you}\:{have}\:{only}\:{one}\:{letter}\:{S}. \\ $$
Commented by Tawa11 last updated on 14/Oct/22
Great sir
$$\mathrm{Great}\:\mathrm{sir} \\ $$
Commented by Acem last updated on 14/Oct/22
Good morning sir! At first, and f.e. if we choose the letters {a, f, t, l} and f.e. again if we formed the word “Flat” and we know that there′s two of both of t, a in this case we will get duplicate words, with this in mind, i made an exception for repeatation and i started with 7 letters to say that the numbers of words are 7^4 = 2401 2nd If i was wrong, please explain to me why 3rd If your solution was correct, please explain the steps 2, 3 and 4 in detail, and of course when you have enough time.
$${Good}\:{morning}\:{sir}! \\ $$$${At}\:{first},\:{and}\:{f}.{e}.\:{if}\:{we}\:{choose}\:{the}\:{letters}\:\left\{{a},\:{f},\:{t},\:{l}\right\} \\ $$$$\:{and}\:{f}.{e}.\:{again}\:{if}\:{we}\:{formed}\:{the}\:{word}\:“{Flat}'' \\ $$$$\:{and}\:{we}\:{know}\:{that}\:{there}'{s}\:{two}\:{of}\:{both}\:{of}\:{t},\:{a} \\ $$$$\:{in}\:{this}\:{case}\:{we}\:{will}\:{get}\:{duplicate}\:{words},\:{with}\:{this} \\ $$$$\:{in}\:{mind},\:{i}\:{made}\:{an}\:{exception}\:{for}\:{repeatation} \\ $$$$\:{and}\:{i}\:{started}\:{with}\:\mathrm{7}\:{letters}\:{to}\:{say}\:{that}\:{the} \\ $$$$\:{numbers}\:{of}\:{words}\:{are}\:\mathrm{7}^{\mathrm{4}} =\:\mathrm{2401} \\ $$$$ \\ $$$$\mathrm{2}{nd}\:{If}\:{i}\:{was}\:{wrong},\:{please}\:{explain}\:{to}\:{me}\:{why} \\ $$$$ \\ $$$$\mathrm{3}{rd}\:{If}\:{your}\:{solution}\:{was}\:{correct},\:{please}\:{explain} \\ $$$$\:{the}\:{steps}\:\mathrm{2},\:\mathrm{3}\:{and}\:\mathrm{4}\:{in}\:{detail},\:{and}\:{of}\:{course}\:{when} \\ $$$$\:{you}\:{have}\:{enough}\:{time}. \\ $$$$ \\ $$
Commented by mr W last updated on 14/Oct/22
with 7 different letters you can only form 7×6×5×4=840 words, not 7^4 . we have only two letters a and two letters t, therefore we can only use these two letters twice in a word.
$${with}\:\mathrm{7}\:{different}\:{letters}\:{you}\:{can}\:{only} \\ $$$${form}\:\mathrm{7}×\mathrm{6}×\mathrm{5}×\mathrm{4}=\mathrm{840}\:{words},\:{not} \\ $$$$\mathrm{7}^{\mathrm{4}} . \\ $$$${we}\:{have}\:{only}\:{two}\:{letters}\:{a}\:{and}\:{two}\: \\ $$$${letters}\:{t},\:{therefore}\:{we}\:{can}\:{only}\:{use} \\ $$$${these}\:{two}\:{letters}\:{twice}\:{in}\:{a}\:{word}. \\ $$
Commented by mr W last updated on 14/Oct/22
i have added some explanation in my solution above.
$${i}\:{have}\:{added}\:{some}\:{explanation}\:{in}\:{my} \\ $$$${solution}\:{above}. \\ $$
Commented by Acem last updated on 14/Oct/22
I know that with 7 diff. lett. we get 840, i meant to exclude the repetition of t, a so N_(words) = 7^4 to avoid getting Flat_(for exampke) three times
$${I}\:{know}\:{that}\:{with}\:\mathrm{7}\:{diff}.\:{lett}.\:{we}\:{get}\:\mathrm{840},\:{i}\:{meant} \\ $$$$\:{to}\:{exclude}\:{the}\:{repetition}\:{of}\:{t},\:{a}\:\:{so}\:{N}_{{words}} =\:\mathrm{7}^{\mathrm{4}} \:{to} \\ $$$$\:{avoid}\:{getting}\:{Flat}_{{for}\:{exampke}} \:{three}\:{times} \\ $$
Commented by Acem last updated on 14/Oct/22
Note: I modified the question with “different words” because there is no point in repeating the results”Therefore the solution will change too.
$${Note}:\:{I}\:{modified}\:{the}\:{question}\:{with} \\ $$$$\:“{different}\:{words}''\:{because}\:{there}\:{is}\:{no}\:{point} \\ $$$$\:{in}\:{repeating}\:{the}\:{results}''{Therefore}\:{the}\:{solution} \\ $$$$\:{will}\:{change}\:{too}. \\ $$$$\: \\ $$
Commented by Acem last updated on 15/Oct/22
According to your logic, the group of the alphabet would be unable to make words of 4 letters like: room, will, cick, rare..etc
$${According}\:{to}\:{your}\:{logic},\:{the}\:{group}\:{of}\:{the}\:{alphabet} \\ $$$$\:{would}\:{be}\:{unable}\:{to}\:{make}\:{words}\:{of}\:\mathrm{4}\:{letters}\:{like}: \\ $$$$\:{room},\:{will},\:{cick},\:{rare}..{etc} \\ $$$$ \\ $$
Commented by mr W last updated on 14/Oct/22
to me “how many words” means automatically “how many different words”.
$${to}\:{me}\:“{how}\:{many}\:{words}''\:{means}\: \\ $$$${automatically}\:“{how}\:{many}\:{different} \\ $$$${words}''. \\ $$
Commented by Acem last updated on 14/Oct/22
Good! about this i agree with you. And let′s start over, to narrow down the choice′s idea with a simple example: If we want form words of 3 letters_(sure i didn′t say diff.) of the word ”Syria” i can say 5^3 = 125 Till now is that ok?... am waiting for your replay
$${Good}!\:{about}\:{this}\:\:{i}\:{agree}\:{with}\:{you}.\:{And}\:{let}'{s}\:{start} \\ $$$$\:{over},\:{to}\:{narrow}\:{down}\:{the}\:{choice}'{s}\:{idea}\:{with}\:{a} \\ $$$$\:{simple}\:{example}: \\ $$$$ \\ $$$${If}\:{we}\:{want}\:{form}\:{words}\:{of}\:\mathrm{3}\:{letters}_{{sure}\:{i}\:{didn}'{t}\:{say}\:{diff}.} \\ $$$$\:{of}\:{the}\:{word}\:''{Syria}''\:{i}\:{can}\:{say}\:\mathrm{5}^{\mathrm{3}} =\:\mathrm{125} \\ $$$$ \\ $$$$\:{Till}\:{now}\:{is}\:{that}\:{ok}?…\:{am}\:{waiting}\:{for}\:{your}\:{replay} \\ $$$$ \\ $$
Commented by Acem last updated on 15/Oct/22
But here the repetition is allowed as long as we didn′t say words of 3 different letters. This is like when we draw a thing with returning
$${But}\:{here}\:{the}\:{repetition}\:{is}\:{allowed}\:{as}\:{long}\:{as}\:{we} \\ $$$$\:{didn}'{t}\:{say}\:{words}\:{of}\:\mathrm{3}\:{different}\:{letters}. \\ $$$$\:{This}\:{is}\:{like}\:{when}\:{we}\:{draw}\:{a}\:{thing}\: \\ $$$$\:\:{with}\:{returning} \\ $$
Commented by mr W last updated on 15/Oct/22
we want to form the words using the letters SYRIA, we have only these 5 letters to use. the words formed have automatically different letters. when we want to form the words using the letters flatearth, we have only these 9 letters to use. the words formed may also have same letters, for example 2 a or 2 t. if you want to understand otherwise, you can do.
$${we}\:{want}\:{to}\:{form}\:{the}\:{words}\:{using} \\ $$$${the}\:{letters}\:{SYRIA},\:{we}\:{have}\:{only}\:{these} \\ $$$$\mathrm{5}\:{letters}\:{to}\:{use}.\:{the}\:{words}\:{formed}\:{have} \\ $$$${automatically}\:{different}\:{letters}. \\ $$$${when}\:{we}\:{want}\:{to}\:{form}\:{the}\:{words}\:{using} \\ $$$${the}\:{letters}\:{flatearth},\:{we}\:{have}\:{only} \\ $$$${these}\:\mathrm{9}\:{letters}\:{to}\:{use}.\:{the}\:{words}\:{formed} \\ $$$${may}\:{also}\:{have}\:{same}\:{letters},\:{for}\: \\ $$$${example}\:\mathrm{2}\:{a}\:{or}\:\mathrm{2}\:{t}. \\ $$$${if}\:{you}\:{want}\:{to}\:{understand}\:{otherwise}, \\ $$$${you}\:{can}\:{do}. \\ $$
Commented by mr W last updated on 15/Oct/22
i won′t waste my time any more for discussing such non−sense sir.
$${i}\:{won}'{t}\:{waste}\:{my}\:{time}\:{any}\:{more}\:{for} \\ $$$${discussing}\:{such}\:{non}−{sense}\:{sir}. \\ $$
Commented by SLVR last updated on 15/Oct/22
nice...sir
$${nice}…{sir} \\ $$

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *