Answer
(a) 416,965,528
(b) 113,588,800
(c) 130,721,752
Work Step by Step
(a) The number of samples of size five is $\frac{140!}{5! 135!} = 416,965,528$
(b) There are 10 ways of selecting one nonconforming chip and there are $\frac{130!}{4! 126!} = 11,358,880$ ways of selecting four conforming chips. Therefore, the number of samples that contain exactly one
nonconforming chip is $10 \times \frac{130!}{4! 126!} = 113,588,800$
(c) The number of samples that contain at least one nonconforming chip is the total number of samples $140C5$ minus the number of samples that contain no nonconforming chips $130C5$. Threfore,
$\frac{140!}{5! 135!} - \frac{130!}{5! 125!} = 130,721,752$
