Question

find the value of each of these quantities.
C(5,3)
C(8,8)
C(12,6)

Answer 1

$C^n_k= \frac{n!}{(n-k)!c!} \\ \\C^5_3= \frac{5!}{(5-3)!3!} = \frac{5!}{2!3!} = \frac{5\times4\times3}{3\times2\times1} =10 \\ \\C^8_8= \frac{8!}{(8-8)!8!} = \frac{8!}{0!8!} = \frac{8!}{1\times8!}=1 \\ \\C^{12}_6= \frac{12!}{(12-6)!6!} = \frac{12!}{6!6!} = \frac{12\times11\times10\times9\times8\times7}{6\times5\times4\times3\times2\times1} =\frac{11\times3\times4\times7}{1} =924$