Category: Permutation and Combination

Question Number 190260 by alcohol last updated on 30/Mar/23 $$f:[1,3]\to \mathbb{R},f\left(x\right)=\frac{1}{x}$$$$A(1,1)$$$$B(1,\frac{1}{3})$$$$B^{\prime }(b,\frac{1}{b}),b⩾1$$$$Find$$$$i.equationofline{AB}^{\prime }$$$$ii.equationoftangentT{}^{\prime }to{C}_{f}atpoint$$$${with}\:{x}\:=\:\frac{\mathrm{1}\:+\:{b}}{\mathrm{2}}…

Question Number 124709 by benjo_mathlover last updated on 05/Dec/20 $$Between20000and70000$$$$findthenumberofevenintegers$$$$inwhichnodigitsisrepeated$$ Answered by liberty last updated on 05/Dec/20 $${Let}\:{abcde}\:{be}\:{a}\:{required}\:{even}\:{integer}.\: \…

Question Number 59021 by mr W last updated on 03/May/19 $$\left[Q58885reposted\right]$$$$Howmany4-digitnumbersabcdexist$$$$whicharedivisibleby3andsatisfy$$$$a⩽b⩽c⩽d?$$ Commented by tanmay last updated on…

Question Number 124372 by mr W last updated on 02/Dec/20 $$Howmanysix-digitnumberscontain$$$$exactlysixdifferentdigits?$$ Answered by bemath last updated on 02/Dec/20 $$=\:\mathrm{9}×{P}_{\mathrm{5}} ^{\:\mathrm{9}} \:=\:\mathrm{9}×\frac{\mathrm{9}!}{\mathrm{4}!}…

Question Number 124173 by bramlexs22 last updated on 01/Dec/20 Answered by bobhans last updated on 01/Dec/20 $$(1+kx){(1-2x)}^5=(1+kx)\left[\underset{n=0}{\sum ^5}{C}_n^5{(-2x)}^{5-n}\right]$$$$=\left(\mathrm{1}+{kx}\right)\left({C}_{\mathrm{3}}…