Category: Permutation and Combination

Question Number 142618 by iloveisrael last updated on 03/Jun/21 $$Inhowmanywayscancommittee$$$$of5beformedfromagroup$$$$of11peopleconsistingof4teachers$$$$and7studentsifthereisno$$$$restrictionintheselection?$$$$\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}$$ Commented by som(math1967)…

Question Number 11384 by tawa last updated on 22/Mar/17 $$\mathrm{Out}\mathrm{of}5\mathrm{accountants}\mathrm{and}7\mathrm{bankers},\mathrm{a}\mathrm{committee}\mathrm{consisting}\mathrm{of}$$$$2\mathrm{accountants}\mathrm{and}3\mathrm{bankers}\mathrm{is}\mathrm{to}\mathrm{be}\mathrm{formed}.\mathrm{In}\mathrm{how}\mathrm{many}\mathrm{ways}\mathrm{can}\mathrm{this}$$$$\mathrm{be}\mathrm{done}\mathrm{if}$$$$\left(\mathrm{a}\right)\mathrm{Any}\mathrm{acountant}\mathrm{and}\mathrm{any}\mathrm{bankers}\mathrm{must}\mathrm{be}\mathrm{included}$$$$\left(\mathrm{b}\right)\mathrm{One}\mathrm{particular}\mathrm{banker}\mathrm{must}\mathrm{be}\mathrm{included}$$$$\left(\mathrm{c}\right)2\mathrm{accountant}\mathrm{cannot}\mathrm{be}\mathrm{in}\mathrm{the}\mathrm{committee}$$ Answered by sandy_suhendra…

Question Number 142305 by anonymo last updated on 29/May/21 Answered by Olaf_Thorendsen last updated on 01/Jun/21 $${(1+i)}^{80}=\underset{p=0}{\sum ^{80}}{\mathrm{C}}_p^{80}{i}^p$$$$\left(\mathrm{1}+{i}\right)^{\mathrm{80}} \:=\:\underset{{k}=\mathrm{0}}…

Question Number 141435 by physicstutes last updated on 18/May/21 $$\mathrm{Find}\mathrm{all}\mathrm{the}\mathrm{arraangment}\mathrm{of}\mathrm{all}\mathrm{the}\mathrm{letters}$$$$\mathrm{of}\mathrm{the}\mathrm{word}\mathrm{SYLLABUSES}\mathrm{such}\mathrm{that}$$$$\mathrm{each}\mathrm{word}\mathrm{contains}\mathrm{the}\mathrm{word}\mathrm{BUS}.$$ Answered by mr W last updated on 19/May/21 $$\mathrm{SYLLABUSES}…

Question Number 9747 by tawakalitu last updated on 30/Dec/16 $$\mathrm{Find}\mathrm{the}\mathrm{coefficient}\mathrm{of}\mathrm{the}\mathrm{term}\mathrm{independent}$$$$\mathrm{of}\mathrm{x}\mathrm{in}\mathrm{the}\mathrm{expansion}\mathrm{of}$$$${(\frac{\mathrm{x}+1}{{\mathrm{x}}^{2/3}-{\mathrm{x}}^{1/3}+1}-\frac{\mathrm{x}-1}{\mathrm{x}-{\mathrm{x}}^{1/2}})}^{10}$$ Answered by sandy_suhendra last updated on…