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Category: Permutation and Combination

In-the-square-PQRS-K-is-the-midpoint-of-PQ-L-is-the-midpoint-of-QR-M-is-the-midpoint-RS-N-is-the-midpoint-of-SP-and-O-is-the-midpoint-of-KM-A-line-segment-is-drawn-from-each-pair-of-points-from-

Question Number 110523 by Aina Samuel Temidayo last updated on 29/Aug/20 $$ \\ $$$$\mathrm{In}\:\mathrm{the}\:\mathrm{square}\:\mathrm{PQRS},\:\mathrm{K}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{midpoint}\:\mathrm{of}\:\mathrm{PQ},\:\mathrm{L}\:\mathrm{is}\:\mathrm{the}\:\mathrm{midpoint}\:\mathrm{of} \\ $$$$\mathrm{QR},\:\mathrm{M}\:\mathrm{is}\:\mathrm{the}\:\mathrm{midpoint}\:\mathrm{RS},\:\mathrm{N}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{midpoint}\:\mathrm{of}\:\mathrm{SP}\:\mathrm{and}\:\mathrm{O}\:\mathrm{is}\:\mathrm{the}\:\mathrm{midpoint} \\ $$$$\mathrm{of}\:\mathrm{KM}.\:\mathrm{A}\:\mathrm{line}\:\mathrm{segment}\:\mathrm{is}\:\mathrm{drawn}\:\mathrm{from} \\ $$$$\mathrm{each}\:\mathrm{pair}\:\mathrm{of}\:\mathrm{points}\:\mathrm{from} \\…

How-many-ways-can-the-letters-in-the-word-MATHEMATICS-be-rearranged-such-that-the-word-formed-either-starts-or-ends-with-a-vowel-and-any-three-consecutive-letters-must-contain-a-vowel-

Question Number 110498 by Aina Samuel Temidayo last updated on 29/Aug/20 $$\mathrm{How}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{the}\:\mathrm{letters}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{word}\:\mathrm{MATHEMATICS}\:\mathrm{be} \\ $$$$\mathrm{rearranged}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{word}\:\mathrm{formed} \\ $$$$\mathrm{either}\:\mathrm{starts}\:\mathrm{or}\:\mathrm{ends}\:\mathrm{with}\:\mathrm{a}\:\mathrm{vowel},\:\mathrm{and} \\ $$$$\mathrm{any}\:\mathrm{three}\:\mathrm{consecutive}\:\mathrm{letters}\:\mathrm{must} \\ $$$$\mathrm{contain}\:\mathrm{a}\:\mathrm{vowel}? \\ $$ Commented…

in-how-many-ways-can-you-put-40-identical-balls-into-20-identical-boxes-such-that-each-box-obtains-at-least-one-ball-and-at-most-5-balls-

Question Number 175567 by mr W last updated on 02/Sep/22 $${in}\:{how}\:{many}\:{ways}\:{can}\:{you}\:{put}\:\mathrm{40} \\ $$$${identical}\:{balls}\:{into}\:\mathrm{20}\:{identical}\:{boxes} \\ $$$${such}\:{that}\:{each}\:{box}\:{obtains}\:{at}\:{least}\:{one} \\ $$$${ball}\:{and}\:{at}\:{most}\:\mathrm{5}\:{balls}? \\ $$ Terms of Service Privacy Policy Contact:…

How-many-are-the-permutations-of-1-a-little-rubik-s-cube-with-4-squares-by-side-2-a-classical-one-with-9-squares-by-side-

Question Number 109488 by bubugne last updated on 24/Aug/20 $${How}\:{many}\:{are}\:{the}\:{permutations}\:{of} \\ $$$$\mathrm{1}\:−\:{a}\:{little}\:{rubik}'{s}\:{cube}\:{with}\:\mathrm{4}\:{squares}\:{by}\:{side} \\ $$$$\mathrm{2}\:−\:{a}\:{classical}\:{one}\:{with}\:\mathrm{9}\:{squares}\:{by}\:{side} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

SUCCESSFULLY-How-many-different-words-can-you-form-using-these-letters-so-that-no-two-same-letters-are-adjacent-

Question Number 109387 by mr W last updated on 19/Sep/20 $$\boldsymbol{\mathrm{SUCCESSFULLY}} \\ $$$${How}\:{many}\:{different}\:{words}\:{can}\:{you} \\ $$$${form}\:{using}\:{these}\:{letters}\:{so}\:{that}\:{no} \\ $$$${two}\:{same}\:{letters}\:{are}\:{adjacent}? \\ $$ Commented by bobhans last updated on…

Question-43824

Question Number 43824 by Necxx last updated on 15/Sep/18 Answered by MJS last updated on 16/Sep/18 $$\left(\frac{\mathrm{1}}{\mathrm{2}}\right)!=\frac{\sqrt{\pi}}{\mathrm{2}} \\ $$$$\left(\frac{\mathrm{1}}{\mathrm{2}}\right)!+\left(\frac{\mathrm{1}}{\mathrm{2}}\right)!=\sqrt{\pi} \\ $$$$\left(\mathrm{A}\right)\:\mathrm{1}!=\mathrm{1} \\ $$$$\left(\mathrm{B}\right)\:\:\mathrm{sin}\:\mathrm{45}°\:=\frac{\sqrt{\mathrm{2}}}{\mathrm{2}} \\ $$$$\left(\mathrm{C}\right)\:\:\sqrt{\mathrm{arccos}\:−\mathrm{1}}=\sqrt{\pi}…

Find-the-number-of-ways-a-committee-of-4-people-can-be-chosen-from-a-group-of-5-men-and-7-women-when-it-contains-people-of-both-sexes-and-there-are-at-least-as-many-women-as-men-

Question Number 174855 by byaw last updated on 12/Aug/22 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\: \\ $$$$\mathrm{a}\:\mathrm{committee}\:\mathrm{of}\:\mathrm{4}\:\mathrm{people}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{chosen}\:\mathrm{from}\:\mathrm{a}\:\mathrm{group}\:\mathrm{of}\:\mathrm{5}\:\mathrm{men} \\ $$$$\mathrm{and}\:\mathrm{7}\:\mathrm{women}\:\mathrm{when}\:\mathrm{it}\:\mathrm{contains} \\ $$$$\mathrm{people}\:\mathrm{of}\:\mathrm{both}\:\mathrm{sexes}\:\mathrm{and} \\ $$$$\mathrm{there}\:\mathrm{are}\:\mathrm{at}\:\mathrm{least}\:\mathrm{as}\:\mathrm{many} \\ $$$$\mathrm{women}\:\mathrm{as}\:\mathrm{men}. \\ $$ Answered…

An-unfair-coin-with-the-probability-of-getting-head-in-one-toss-1-5-If-coin-tosses-n-times-the-probability-of-getting-2-heads-is-equal-to-the-probability-of-getting-3-heads-Find-n-

Question Number 43659 by Joel578 last updated on 13/Sep/18 $$\mathrm{An}\:\mathrm{unfair}\:\mathrm{coin}\:\mathrm{with}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of}\:\mathrm{getting} \\ $$$$\mathrm{head}\:\mathrm{in}\:\mathrm{one}\:\mathrm{toss}\:=\:\frac{\mathrm{1}}{\mathrm{5}}. \\ $$$$\mathrm{If}\:\mathrm{coin}\:\mathrm{tosses}\:{n}\:\mathrm{times},\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of} \\ $$$$\mathrm{getting}\:\mathrm{2}\:\mathrm{heads}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of}\: \\ $$$$\mathrm{getting}\:\mathrm{3}\:\mathrm{heads}.\:\mathrm{Find}\:{n} \\ $$ Commented by math1967 last updated…

how-many-odd-numbers-greater-than-60000-can-be-made-from-the-digits-5-6-7-8-9-0-if-no-number-contains-any-digit-more-than-once-

Question Number 43343 by pieroo last updated on 10/Sep/18 $$\mathrm{how}\:\mathrm{many}\:\mathrm{odd}\:\mathrm{numbers}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{60000}\:\mathrm{can}\:\mathrm{be}\:\mathrm{made} \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{5},\mathrm{6},\mathrm{7},\mathrm{8},\mathrm{9},\mathrm{0}\:\mathrm{if}\:\mathrm{no}\:\mathrm{number}\:\mathrm{contains} \\ $$$$\mathrm{any}\:\mathrm{digit}\:\mathrm{more}\:\mathrm{than}\:\mathrm{once}? \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 10/Sep/18 $$\underset{\mathrm{5}} {−}\:\underset{\mathrm{4}}…