Question

Find the value of ${{}^{8}P}_7,{{}^{25}P}_5,{{}^{24}C}_4,{{}^{19}C}_{14}$.

Answer 1

${}^n{P}_r=\frac{n!}{(n-r)!}$

(1) ${}^8{P}_7=\frac{8!}{1!}=8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=40,320$

(2) ${}^{25}{P}_5=\frac{25!}{20!}=25\times 24\times 23\times 22\times 21=6,375,600$

${}^n{C}_r=\frac{n!}{r!(n-r)!}$

(3) ${}^{24}{C}_4=\frac{24!}{4!20!}=\frac{24\times 23\times 22\times 21}{4\times 3\times 2\times 1}=10,626$

(4) ${}^{19}{C}_{14}=\frac{19!}{14!5!}=\frac{19\times 18\times 17\times 16\times 15}{5\times 4\times 3\times 2\times 1}=11,628$