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Category: Permutation and Combination

1-There-are-20-boys-and-10-girls-in-a-class-If-a-committee-of-6-is-to-be-chosen-at-random-having-atleast-2-boys-and-2-girls-find-the-probability-that-i-there-ara-3-boys-in-the-committee-ii-the

Question Number 27270 by das47955@mail.com last updated on 05/Jan/18 $$\left(\mathrm{1}\right)\:\boldsymbol{\mathrm{There}}\:\boldsymbol{\mathrm{are}}\:\mathrm{20}\:\boldsymbol{\mathrm{boys}}\:\boldsymbol{\mathrm{and}}\:\mathrm{10}\:\boldsymbol{\mathrm{girls}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{a}} \\ $$$$\boldsymbol{\mathrm{class}}.\boldsymbol{\mathrm{If}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{committee}}\:\boldsymbol{\mathrm{of}}\:\mathrm{6}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{be}} \\ $$$$\boldsymbol{\mathrm{chosen}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{random}}\:\boldsymbol{\mathrm{having}}\:\boldsymbol{\mathrm{atleast}} \\ $$$$\mathrm{2}\:\boldsymbol{\mathrm{boys}}\:\boldsymbol{\mathrm{and}}\:\mathrm{2}\:\boldsymbol{\mathrm{girls}},\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\: \\ $$$$\boldsymbol{\mathrm{probability}}\:\boldsymbol{\mathrm{that}} \\ $$$$\left(\boldsymbol{\mathrm{i}}\right)\:\boldsymbol{\mathrm{there}}\:\boldsymbol{\mathrm{ara}}\:\mathrm{3}\:\boldsymbol{\mathrm{boys}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{the}}\: \\ $$$$\boldsymbol{\mathrm{committee}} \\ $$$$\left(\boldsymbol{\mathrm{ii}}\right)\:\boldsymbol{\mathrm{there}}\:\boldsymbol{\mathrm{are}}\:\mathrm{4}\:\boldsymbol{\mathrm{boys}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{the}}\: \\…

Calculate-this-problem-below-a-7-5-1-b-5-3-4-c-6-4-d-7-3-2-5-

Question Number 157980 by zainaltanjung last updated on 30/Oct/21 $$\mathrm{Calculate}\:\mathrm{this}\:\mathrm{problem}\:\mathrm{below} \\ $$$$\left.\:\:\:\:\:\:\:\:\mathrm{a}\right).\:\:\frac{\mathrm{7}!}{\left(\mathrm{5}−\mathrm{1}\right)!}\:=…… \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:\mathrm{b}\right).\:\:\frac{\mathrm{5}!×\mathrm{3}!}{\mathrm{4}!}\:=…… \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:\:\mathrm{c}\right).\:\:\mathrm{6}!\:\mathrm{4}!\:=…\:\:\:\:\:\:\:\: \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:\:\mathrm{d}\right).\:\:\frac{\mathrm{7}!}{\mathrm{3}!}×\frac{\mathrm{2}!}{\mathrm{5}!}\:=…… \\ $$ Answered by puissant last updated…

2-Find-the-middle-trem-s-in-the-expansion-of-following-x-2-1-x-3-14-

Question Number 26554 by das47955@mail.com last updated on 26/Dec/17 $$\left(\mathrm{2}\right)\:\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{middle}}\:\boldsymbol{\mathrm{trem}}\left(\boldsymbol{\mathrm{s}}\right)\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{expansion}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{following}}− \\ $$$$\:\:\:\:\:\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}^{\mathrm{3}} }\right)^{\mathrm{14}} \\ $$ Answered by prakash jain last updated on…

2-Find-the-10th-trem-in-the-expansion-of-2x-y-2-

Question Number 26555 by das47955@mail.com last updated on 26/Dec/17 $$\left(\mathrm{2}\right)\:\:\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\mathrm{10}\boldsymbol{\mathrm{th}}\:\boldsymbol{\mathrm{trem}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{expansion}}\:\boldsymbol{\mathrm{of}}\:\left(\mathrm{2}\boldsymbol{\mathrm{x}}−\frac{\boldsymbol{\mathrm{y}}}{\mathrm{2}}\right) \\ $$ Commented by Rasheed.Sindhi last updated on 27/Dec/17 $$\left(\mathrm{2}\boldsymbol{\mathrm{x}}−\frac{\boldsymbol{\mathrm{y}}}{\mathrm{2}}\right)^{?} \\ $$ Terms…

A-number-of-four-different-digits-is-formed-by-using-the-digits-1-2-3-4-5-6-7-in-all-possible-ways-each-digit-occuring-once-only-find-how-many-of-them-are-greater-than-3400-

Question Number 26477 by NECx last updated on 26/Dec/17 $${A}\:{number}\:{of}\:{four}\:{different} \\ $$$${digits}\:{is}\:{formed}\:{by}\:{using}\:{the}\: \\ $$$${digits}\:\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6},\mathrm{7},{in}\:{all}\:{possible} \\ $$$${ways}\:{each}\:{digit}\:{occuring}\:{once} \\ $$$${only}.{find}\:{how}\:{many}\:{of}\:{them}\:{are} \\ $$$${greater}\:{than}\:\mathrm{3400} \\ $$ Answered by mrW1…

Find-the-number-of-all-possible-different-words-into-which-the-word-INTERFERE-can-be-converted-by-change-of-place-of-letters-if-no-two-consonants-must-be-together-

Question Number 26480 by NECx last updated on 26/Dec/17 $${Find}\:{the}\:{number}\:{of}\:{all}\:{possible} \\ $$$${different}\:{words}\:{into}\:{which}\:{the} \\ $$$${word}\:{INTERFERE}\:{can}\:{be}\: \\ $$$${converted}\:{by}\:{change}\:{of}\:{place}\:{of}\: \\ $$$${letters},{if}\:{no}\:{two}\:{consonants} \\ $$$${must}\:{be}\:{together}. \\ $$ Answered by mrW1…

How-many-numbers-less-than-1000-and-divisible-by-5-can-be-formed-with-the-digits-0-1-2-3-4-5-6-7-8-9-each-digit-not-occuring-more-than-once-in-each-number-

Question Number 26473 by NECx last updated on 25/Dec/17 $${How}\:{many}\:{numbers}\:{less}\:{than} \\ $$$$\mathrm{1000}\:{and}\:{divisible}\:{by}\:\mathrm{5}\:{can}\:{be} \\ $$$${formed}\:{with}\:{the}\:{digits}\:\mathrm{0},\:\mathrm{1},\:\mathrm{2}\:,\mathrm{3}\:,\mathrm{4}\:,\mathrm{5}\: \\ $$$$\mathrm{6}\:,\mathrm{7}\:,\mathrm{8}\:,\mathrm{9},{each}\:{digit}\:{not}\:{occuring} \\ $$$${more}\:{than}\:{once}\:{in}\:{each}\:{number}? \\ $$ Answered by mrW1 last updated…

how-many-ways-can-you-exchange-1-dollar-using-1-5-10-25-50-cents-example-1-dollar-100-cents-2-50cents-1-50-2-25-4-25-1-50-1-25-1-10-1-5-10-1-and-so-on-how-many-all-the-ways-

Question Number 157126 by malwan last updated on 20/Oct/21 $${how}\:{many}\:{ways}\:{can}\:{you} \\ $$$${exchange}\:\mathrm{1}\:{dollar}\:{using} \\ $$$$\left(\mathrm{1},\mathrm{5},\mathrm{10},\mathrm{25},\mathrm{50}\right)\:{cents} \\ $$$${example} \\ $$$$\mathrm{1}\:{dollar}\left(\mathrm{100}\:{cents}\right)=\mathrm{2}×\mathrm{50}{cents} \\ $$$$=\mathrm{1}×\mathrm{50}+\mathrm{2}×\mathrm{25}=\mathrm{4}×\mathrm{25} \\ $$$$=\mathrm{1}×\mathrm{50}+\mathrm{1}×\mathrm{25}+\mathrm{1}×\mathrm{10}+\mathrm{1}×\mathrm{5}+\mathrm{10}×\mathrm{1} \\ $$$${and}\:{so}\:{on} \\…