Question and Answers Forum

Permutation and CombinationQuestion and Answers: Page 10

Question Number 132977 Answers: 0 Comments: 0

Show that: ^n C_r =((Π_(k=0) ^(r−1) n−k)/(r!))

$Show that :$ $^{n} C_{r} = \frac{\underset{k = 0}{\prod^{r - 1}} n - k}{r!}$

Question Number 132854 Answers: 1 Comments: 0

It is required to seat 5 men and 4 women in a row so that the women occupy the even place. How many such arrangements are possible ?

$It is required to seat 5 men and 4 women$ $in a row so that the women occupy the even$ $place . How many such arrangements are$ $possible ?$

Question Number 132726 Answers: 0 Comments: 0

use error fxn use polar coordinates to find ∫e^(−x^2 ) dx

$use error fxn$ $use polar coordinates to find$ $\int e^{- x^{2}} dx$

Question Number 132439 Answers: 0 Comments: 1

it is a known that a particular machine will make product with a qualified rate of 90% when it is running well, but will do so with a qualified rate of only 30% when it is not running well. The probability that machine is running well is 75% normally . Suppose that one day the first product made by the machine is qualified. Find the probabiliy that the machine is running well at this time.

$it is a known that a particular$ $machine will make product with$ $a qualified rate of 90 % when it is$ $running well, but will do so with$ $a qualified rate of only 30 % when$ $it is not running well . The$ $probability that machine is$ $running well is 75 % normally .$ $Suppose that one day the first$ $product made by the machine is$ $qualified . Find the probabiliy$ $that the machine is running well at$ $this time .$

Question Number 132382 Answers: 1 Comments: 0

What is the coefficient x^(10) in the expansion of (1+x^2 −x^3 )^8

$What is the coefficient x^{10}$ $in the expansion of {(1 + x^{2} - x^{3})}^{8}$

Question Number 132174 Answers: 0 Comments: 3

Question Number 131994 Answers: 2 Comments: 1

Question Number 131744 Answers: 1 Comments: 0

Question Number 131635 Answers: 0 Comments: 0

three subject group are to be formed randomly by 15 students (including 3 girls) under the condition that each groups consist 5 students and each student attends only one group. flnd the probabilities that of the following events (1) there is exactly one girl in each group (2) the 3 girls attend the same group

$three subject group are to be$ $formed randomly by 15 students$ $(including 3 girls) under the$ $condition that each groups$ $consist 5 students and each$ $student attends only one group .$ $flnd the probabilities that of the$ $following events (1) there is$ $exactly one girl in each group (2)$ $the 3 girls attend the same group$

Question Number 131553 Answers: 1 Comments: 0

Question Number 131464 Answers: 1 Comments: 0

determinant (((old plate : EEU 874)),((new plate : 1BXK 267))) Old California license plate consisted of a sequence of three letters followed by three digits (see figure above). Assuming that any sequence of letters and digits was allowed (though actually some combinations of letters were disallowed), how many license plate were available ?

$\begin{array}{cc} o l d p l a t e : E E U 874 \\ n e w p l a t e : 1 B X K 267 \end{array}$ $O l d C a l i f o r n i a l i c e n s e p l a t e$ $c o n s i s t e d o f a s e q u e n c e o f$ $t h r e e l e t t e r s f o l l o w e d b y t h r e e$ $d i g i t s (s e e f i g u r e a b o v e) .$ $A s s u m i n g t h a t a n y s e q u e n c e$ $o f l e t t e r s a n d d i g i t s w a s a l l o w e d$ $(t h o u g h a c t u a l l y s o m e c o m b i n a t i o n s$ $o f l e t t e r s w e r e d i s a l l o w e d), h o w$ $m a n y l i c e n s e p l a t e w e r e$ $a v a i l a b l e ?$

Question Number 131459 Answers: 1 Comments: 0

Eight eligible bachelor and seven beautiful models happen randomly to have purchased single seats in the same 15−seats row of theather. On the average , how many pairs of adjacent seats are ticketed for marriageable couples ?

$E i g h t e l i g i b l e b a c h e l o r a n d s e v e n b e a u t i f u l$ $m o d e l s h a p p e n r a n d o m l y t o h a v e$ $p u r c h a s e d s i n g l e s e a t s i n t h e s a m e 15 - s e a t s$ $r o w o f t h e a t h e r . O n t h e a v e r a g e, h o w m a n y$ $p a i r s o f a d j a c e n t s e a t s a r e t i c k e t e d$ $f o r m a r r i a g e a b l e c o u p l e s ?$

Question Number 131248 Answers: 2 Comments: 0

If α and β are the coefficient of x^8 and x^(−24) respectively in the expansion of [ x^4 +2+(1/x^4 ) ]^(10) in powers of x then (α/β) is equal to

$I f α a n d β a r e t h e c o e f f i c i e n t$ $o f x^{8} a n d x^{- 24} r e s p e c t i v e l y$ $i n t h e e x p a n s i o n o f {[x^{4} + 2 + \frac{1}{x^{4}}]}^{10}$ $i n p o w e r s o f x t h e n \frac{α}{β} i s e q u a l t o$

Question Number 131162 Answers: 0 Comments: 2

Five children sitting one behind the other in a five seater merry−go−round ,decide to switch seats so that each child has new companion in front. In how many ways can this be done?

$F i v e c h i l d r e n s i t t i n g o n e b e h i n d$ $t h e o t h e r i n a f i v e s e a t e r m e r r y - g o - r o u n d$ $, d e c i d e t o s w i t c h s e a t s s o t h a t e a c h$ $c h i l d h a s n e w c o m p a n i o n i n f r o n t .$ $I n h o w m a n y w a y s c a n t h i s b e d o n e ?$

Question Number 130899 Answers: 0 Comments: 1

There are 20 persons at a party. Maria dansed with 7 boys, Stacy dansed with 8 boys, Monia dansed with 9 boys and Eve dansed with all the boys at the party. How many girls are there at the party ?

$There are 20 persons at a party .$ $Maria dansed with 7 boys,$ $Stacy dansed with 8 boys,$ $Monia dansed with 9 boys and$ $Eve dansed with all the boys at the party .$ $How many girls are there at the party ?$

Question Number 130685 Answers: 2 Comments: 0

How many password containing 6 characters of the letters in the word ′′ Move Now ′′ ?

$H o w m a n y p a s s w o r d c o n t a i n i n g$ $6 c h a r a c t e r s o f t h e l e t t e r s i n t h e$ $w o r d^{″} M o v e N o w^{″} ?$

Question Number 130689 Answers: 0 Comments: 0

Mr. Rahmat decided to create a password with the form numbers and letterse intermittntly intermittent ( can also be letters and numbers intermittently) but no nmbers and letters are the same. It chooses to use numbers on the set {2, 5, 8, 9} and selects the letters on the set { A, X, Y, W,Z} How many passwords can I create

$Mr . Rahmat decided to create a password$ $with the form numbers and letterse$ $intermittntly intermittent (can also be$ $letters and numbers intermittently) but no$ $nmbers and letters are the same . It$ $chooses to use numbers on the set {2, 5, 8, 9}$ $and selects the letters on the set {A, X, Y, W, Z}$ $How many passwords can I create$

Question Number 130634 Answers: 1 Comments: 0

Question Number 130602 Answers: 1 Comments: 0

Question Number 130193 Answers: 2 Comments: 0

How many words with at least 2 letters can be formed from UNUSUALNESS?

$How many words with at least 2 letters$ $can be formed from UNUSUALNESS ?$

Question Number 130034 Answers: 1 Comments: 0

How many integers between 999 and 4000 (both are included) can be formed using digits 0,1,2,3,4 if repetition of digits is allowed?

$How many integers between 999 and 4000$ $(both are included) can be formed using$ $digits 0, 1, 2, 3, 4 if repetition of digits is$ $allowed ?$

Question Number 130019 Answers: 1 Comments: 0

How many 4 letters word can be formed from COMMUNICATION

$How many 4 letters word can be formed from COMMUNICATION$

Question Number 125548 Answers: 1 Comments: 2

How many four−digit numbers between 2000 and 4000 can be formed from the numbers 0, 1, 2, 3, 4 and 5 if repitition is allowed?

$How many four - digit numbers$ $between 2000 and 4000 can be formed$ $from the numbers 0, 1, 2, 3, 4 and 5$ $if repitition is allowed ?$

Question Number 125460 Answers: 1 Comments: 0

In a room containing N people N>3, at least one person has not shaken hands with everyone else in the room. What is the maximum number of people in the room that could have shaken hands with everyone else?

$I n a r o o m c o n t a i n i n g N p e o p l e$ $N > 3, a t l e a s t o n e p e r s o n h a s n o t$ $s h a k e n h a n d s w i t h e v e r y o n e$ $e l s e i n t h e r o o m . W h a t i s t h e$ $m a x i m u m n u m b e r o f p e o p l e$ $i n t h e r o o m t h a t c o u l d h a v e$ $s h a k e n h a n d s w i t h e v e r y o n e$ $e l s e ?$

Question Number 125208 Answers: 1 Comments: 0

There are 12 students in a party. Five of them are girls. In how many ways can these 12 students be arranged in a row if (i) there are no restrictions? (ii) the 5 girls must be together (forming a block)? (iii) no 2 girls are adjacent (iv) between two particular boys A and B , there no boys but exactly 3 girls?

$T h e r e a r e 12 s t u d e n t s i n a p a r t y . F i v e o f$ $t h e m a r e g i r l s . I n h o w m a n y w a y s c a n$ $t h e s e 12 s t u d e n t s b e a r r a n g e d i n a r o w i f$ $(i) t h e r e a r e n o r e s t r i c t i o n s ?$ $(i i) t h e 5 g i r l s m u s t b e t o g e t h e r (f o r m i n g a b l o c k) ?$ $(i i i) n o 2 g i r l s a r e a d j a c e n t$ $(i v) b e t w e e n t w o p a r t i c u l a r b o y s A a n d B$ $, t h e r e n o b o y s b u t e x a c t l y 3 g i r l s ?$

Question Number 125207 Answers: 2 Comments: 0

Find the number of ways to choose a pair {a,b} of distinct numbers from the set {1,2,3,...,50} such that (i) ∣a−b∣ = 5 (ii) ∣a−b∣ ≤ 5

$F i n d t h e n u m b e r o f w a y s t o c h o o s e a p a i r$ ${a, b} o f d i s t i n c t n u m b e r s f r o m t h e s e t$ ${1, 2, 3, . . ., 50} s u c h t h a t$ $(i) ∣ a - b ∣ = 5$ $(i i) ∣ a - b ∣ ⩽ 5$

Pg 5 Pg 6 Pg 7 Pg 8 Pg 9 Pg 10 Pg 11 Pg 12 Pg 13 Pg 14

Contact: info@tinkutara.com