Menu Close

Category: Permutation and Combination

Question-181251

Question Number 181251 by cortano1 last updated on 23/Nov/22 Commented by cortano1 last updated on 23/Nov/22 $$\:\mathrm{A}\:\mathrm{photograph}\:\mathrm{is}\:\mathrm{to}\:\mathrm{be}\:\mathrm{taken}\:\mathrm{of}\:\mathrm{seven}\:\mathrm{girls}\: \\ $$$$\:\mathrm{standing}\:\mathrm{in}\:\mathrm{two}\:\mathrm{rows},\:\mathrm{with}\:\mathrm{one}\:\mathrm{row} \\ $$$$\mathrm{in}\:\mathrm{front}\:\mathrm{of}\:\mathrm{the}\:\mathrm{other}.\:\mathrm{The}\:\mathrm{tallest}\:\mathrm{girl}\: \\ $$$$\mathrm{must}\:\mathrm{be}\:\mathrm{in}\:\mathrm{the}\:\mathrm{midlle}\:\mathrm{of}\:\mathrm{the}\:\mathrm{row}\:\mathrm{of} \\ $$$$\mathrm{three}\:\mathrm{and}\:\mathrm{the}\:\mathrm{shortest}\:\mathrm{girl}\:\mathrm{must}\:\mathrm{be}…

5-digit-number-divisible-by-3-formed-using-0-1-2-3-4-5-without-repetition-Total-number-of-such-no-s-is-

Question Number 50008 by rahul 19 last updated on 13/Dec/18 $$\mathrm{5}−{digit}\:{number}\:{divisible}\:{by}\:\mathrm{3}\:{formed} \\ $$$${using}\:\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5}\:{without}\:{repetition}. \\ $$$${Total}\:{number}\:{of}\:{such}\:{no}.{s}\:{is}\:? \\ $$ Commented by rahul 19 last updated on 13/Dec/18…

H-n-k-1-n-1-k-show-that-H-2n-H-n-k-1-n-1-2k-1-1-2k-

Question Number 180899 by alcohol last updated on 19/Nov/22 $${H}_{{n}} \:=\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}} \\ $$$${show}\:{that}\:{H}_{\mathrm{2}{n}} \:−\:{H}_{{n}} \:=\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\frac{\mathrm{1}}{\mathrm{2}{k}−\mathrm{1}}−\frac{\mathrm{1}}{\mathrm{2}{k}}\right) \\ $$ Answered by Frix last…

2-women-and-4-men-will-sit-on-the-8-available-seats-and-surround-the-round-table-The-many-possible-arrangements-of-them-sitting-if-they-sat-randomly-

Question Number 115230 by bemath last updated on 24/Sep/20 $$\mathrm{2}\:{women}\:{and}\:\mathrm{4}\:{men}\:{will}\:{sit}\:{on}\:{the} \\ $$$$\mathrm{8}\:{available}\:{seats}\:{and}\:{surround}\: \\ $$$${the}\:{round}\:{table}\:.\:{The}\:{many}\:{possible} \\ $$$${arrangements}\:{of}\:{them}\:{sitting} \\ $$$${if}\:{they}\:{sat}\:{randomly} \\ $$ Commented by mr W last…

1-Given-P-n-1-2n-1-P-n-2n-1-3-5-find-n-2-in-how-many-ways-can-6-persons-stand-in-a-queue-3-how-many-different-4-letter-words-can-be-formed-by-using-letters-of-EDUCATIO

Question Number 115170 by bobhans last updated on 24/Sep/20 $$\left(\mathrm{1}\right){Given}\:\frac{{P}\:_{{n}−\mathrm{1}} ^{\mathrm{2}{n}+\mathrm{1}} }{{P}\:_{{n}} ^{\mathrm{2}{n}−\mathrm{1}} }\:=\:\frac{\mathrm{3}}{\mathrm{5}}\:,\:{find}\:{n}\:=\:? \\ $$$$\left(\mathrm{2}\right)\:{in}\:{how}\:{many}\:{ways}\:{can}\:\mathrm{6}\:{persons} \\ $$$${stand}\:{in}\:{a}\:{queue}? \\ $$$$\left(\mathrm{3}\right)\:{how}\:{many}\:{different}\:\mathrm{4}\:{letter}\:{words} \\ $$$${can}\:{be}\:{formed}\:{by}\:{using}\:{letters}\:{of}\: \\ $$$${EDUCATION}\:{using}\:{each}\:{letter}\:{at}\: \\…