Question

Solve the problem. How many ways can an IRS auditor select 5 of 10 tax returns for an audit?

Answer 1

Answer:

The number of ways an IRS auditor can select 5 of 10 tax returns for an audit is:

                                  252 ways

Step-by-step explanation:

We know that the number of ways of selecting r items from a set of n items is calculated with the help of a combination formula.

i.e.

$n_C_r=\dfrac{n!}{r!\times (n-r)!}$

Here we are asked to find the number of ways  an IRS auditor can elect 5 of 10 tax returns for an audit.

i.e. we have: n=10 and r=5

Hence, the number of ways of doing so is:

${10}_C_5=\dfrac{10!}{5!\times (10-5)!}\\\\i.e.\\\\{10}_C_5=\dfrac{10!}{5!\times 5!}\\\\i.e.\\\\{10}_C_5=\dfrac{10\times 9\times 8\times 7\times 6\times 5!}{5!\times 5!}\\\\i.e.\\\\{10}_C_5=\dfrac{10\times 9\times 8\times 7\times 6}{5!}\\\\i.e.\\\\{10}_C_5=\dfrac{10\times 9\times 8\times 7\times 6}{5\times 4\times 3\times 2}\\\\i.e.\\\\{10}_C_5=252$

Answer 2

Answer:

(12 * 11 * 10 * 9 * 8) / (5 * 4 * 3 * 2 * 1) = 792

Step-by-step explanation: