Question

Problem 2.4 You would like to evaluate the probability of success for testing a batch of n processors. To start out, let's assume that if there is a problem with the batch, exactly 1 out of the n processors are defective. You are willing to test only k of the processors (due to budget or times constraints). (a) How many ways are there of testing k out of n processors

Answer 1

Answer:

The answer is "$\bold{n_{C_{k}}}$"

Step-by-step explanation:

$\to {n_{C_{k}}} = \frac{n!}{K! (n-k)!}$

For Example:

if n=5 and k=2

$\to {5_{C_{2}}} = \frac{5!}{2! (5-2)!}$

          $= \frac{5!}{2! (3)!}\\\\= \frac{5!}{2! \times 3!}\\\\= \frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1 \times 3 \times 2 \times 1}\\\\= \frac{5 \times 4 }{2 \times 1 } \\\\= \frac{5 \times 4 }{2} \\\\= 5 \times 2 \\\\= 10$