Category: Permutation and Combination

Question Number 73346 by TawaTawa last updated on 10/Nov/19 Commented by mathmax by abdo last updated on 10/Nov/19 $$\left.{a}\right)\:\sum_{{k}=\mathrm{0}} ^{{n}} \left(\mathrm{2}+\mathrm{3}{k}\right)^{\mathrm{2}} \:=\mathrm{4}+\sum_{{k}=\mathrm{1}} ^{{n}} \left(\mathrm{4}+\mathrm{12}{k}\:+\mathrm{9}{k}^{\mathrm{2}} \right)…

Question Number 138748 by physicstutes last updated on 17/Apr/21 $$\mathrm{A}\mathrm{committee}\mathrm{of}3\mathrm{members}\mathrm{is}\mathrm{to}\mathrm{be}\mathrm{formed}\mathrm{from}8\mathrm{members}.$$$$\mathrm{Find}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{committees}\mathrm{that}\mathrm{can}\mathrm{be}\mathrm{formed}\mathrm{if}\mathrm{two}\mathrm{particular}$$$$\mathrm{club}\mathrm{members}\mathrm{cannot}\mathrm{both}\mathrm{be}\mathrm{in}\mathrm{a}\mathrm{committee}$$ Answered by mr W last updated on 17/Apr/21 $${C}_{\mathrm{3}}…

Question Number 137943 by john_santu last updated on 08/Apr/21 $$Determinethetermindependent$$$$ofxintheexpansion$$$${(\frac{x+1}{x^{2/3}-x^{1/3}+1}-\frac{x-1}{x-x^{1/2}})}^{10}.$$ Answered by EDWIN88 last updated…

Question Number 6090 by sanusihammed last updated on 13/Jun/16 Answered by Rasheed Soomro last updated on 13/Jun/16 $${}^{x+\frac{y}{2}}{\mathrm{C}}_2=21\wedge {}^{\frac{x+y}{2}}{\mathrm{P}}_2=30$$$${Let}\:\:{x}+\frac{{y}}{\mathrm{2}}={n},\:\:^{{n}} \mathrm{C}_{\mathrm{2}}…

Question Number 137035 by mr W last updated on 29/Mar/21 $$\mathrm{Given}\mathrm{a}10-\mathrm{digit}\mathrm{number}X=1345789026$$$$\mathrm{How}\mathrm{many}10-\mathrm{digit}\mathrm{number}\mathrm{that}\mathrm{can}\mathrm{be}\mathrm{made}$$$$\mathrm{using}\mathrm{every}\mathrm{digit}\mathrm{from}X,\mathrm{with}\mathrm{condition}:$$$$\mathrm{If}\mathrm{a}\mathrm{number}n\mathrm{is}\mathrm{located}\mathrm{in}{k}^{th}\mathrm{position}\mathrm{of}X,\mathrm{then}$$$$\mathrm{the}\mathrm{new}\mathrm{created}\mathrm{number}\mathrm{must}\mathrm{not}\mathrm{contain}$$$$\mathrm{number}n\mathrm{in}{k}^{th}\mathrm{position}$$$$…