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Category: Permutation and Combination

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}\: \\…

there-are-5-points-on-a-line-and-4-points-on-a-parallel-line-how-many-quadrilaterals-can-be-formed-with-these-points-as-vertrices-

Question Number 180585 by mr W last updated on 14/Nov/22 $${there}\:{are}\:\mathrm{5}\:{points}\:{on}\:{a}\:{line}\:{and}\:\mathrm{4}\: \\ $$$${points}\:{on}\:{a}\:{parallel}\:{line}. \\ $$$${how}\:{many}\:{quadrilaterals}\:{can}\:{be}\: \\ $$$${formed}\:{with}\:{these}\:{points}\:{as}\: \\ $$$${vertrices}? \\ $$ Answered by nikif99 last…

Find-number-of-4-letter-words-which-can-be-formed-using-the-letters-of-the-word-ALLAHABAD-such-that-NO-repetition-of-letter-and-word-should-start-either-from-H-or-ends-with-D-

Question Number 49482 by rahul 19 last updated on 07/Dec/18 $${Find}\:{number}\:{of}\:\mathrm{4}−{letter}\:{words}\:{which} \\ $$$${can}\:{be}\:{formed}\:{using}\:{the}\:{letters}\:{of}\: \\ $$$${the}\:{word}\:'{ALLAHABAD}'\:{such}\:{that}: \\ $$$${NO}\:{repetition}\:{of}\:{letter}\:{and}\:{word}\:{should} \\ $$$${start}\:“{either}''\:{from}\:{H}\:“{or}''\:{ends}\:{with}\:{D}\:? \\ $$ Commented by tanmay.chaudhury50@gmail.com last…

The-number-of-triangles-that-can-be-formed-by-5-points-in-a-line-and-3-points-on-a-parralel-line-is-

Question Number 180520 by cortano1 last updated on 13/Nov/22 $$\:\:\:\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{triangles}\: \\ $$$$\:\:\:\mathrm{that}\:\mathrm{can}\:\mathrm{be}\:\mathrm{formed}\:\mathrm{by}\:\mathrm{5}\:\mathrm{points}\: \\ $$$$\:\:\:\mathrm{in}\:\mathrm{a}\:\mathrm{line}\:\mathrm{and}\:\mathrm{3}\:\mathrm{points}\:\mathrm{on}\:\mathrm{a}\:\mathrm{parralel}\:\mathrm{line} \\ $$$$\:\:\:\mathrm{is}\:\_\_\_\: \\ $$ Answered by nikif99 last updated on 13/Nov/22…

Find-the-number-of-all-such-7-digit-no-which-satisfy-conditions-1-divisible-by-3-2-repetition-allowed-3-zero-is-not-used-

Question Number 49408 by rahul 19 last updated on 06/Dec/18 $${Find}\:{the}\:{number}\:{of}\:{all}\:{such}\:\mathrm{7}−{digit} \\ $$$${no}.\:{which}\:{satisfy}\:{conditions}: \\ $$$$\left.\mathrm{1}\right)\:{divisible}\:{by}\:\mathrm{3} \\ $$$$\left.\mathrm{2}\right)\:{repetition}\:{allowed} \\ $$$$\left.\mathrm{3}\right)\:{zero}\:{is}\:{not}\:{used}. \\ $$ Commented by mr W…

The-integers-between-1-to-10-4-contain-exactly-one-8-and-one-9-is-I-got-1160-but-one-is-arguing-1154only-kindly-help-me-out-

Question Number 180335 by SLVR last updated on 10/Nov/22 $${The}\:{integers}\:{between}\:\mathrm{1}\:{to}\:\mathrm{10}^{\mathrm{4}} \\ $$$${contain}\:{exactly}\:{one}\:\mathrm{8}\:\:{and}\:{one}\:\mathrm{9} \\ $$$${is}?\:{I}\:{got}\:\mathrm{1160}\:{but}\:{one}\:\:{is}\:{arguing} \\ $$$$\mathrm{1154}{only}..{kindly}\:{help}\:{me}\:{out} \\ $$ Commented by mr W last updated on…

There-are-6-people-going-to-sit-in-a-circle-The-number-of-arrangements-they-sit-if-there-are-2-people-who-always-sit-next-to-each-other-

Question Number 114797 by bemath last updated on 21/Sep/20 $${There}\:{are}\:\mathrm{6}\:{people}\:{going}\:{to}\:{sit}\:{in}\: \\ $$$${a}\:{circle}\:.\:{The}\:{number}\:{of}\:{arrangements} \\ $$$${they}\:{sit}\:{if}\:{there}\:{are}\:\mathrm{2}\:{people}\:{who} \\ $$$${always}\:{sit}\:{next}\:{to}\:{each}\:{other} \\ $$ Answered by mr W last updated on…