Question

Solve the problem.

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

Answer 1

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

Explanation:

Answer 2

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

252 ways

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=(n!)/(r!* (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=(10!)/(5!* (10-5)!)\\\\i.e.\\\\{10}_C_5=(10!)/(5!* 5!)\\\\i.e.\\\\{10}_C_5=(10* 9* 8* 7* 6* 5!)/(5!* 5!)\\\\i.e.\\\\{10}_C_5=(10* 9* 8* 7* 6)/(5!)\\\\i.e.\\\\{10}_C_5=(10* 9* 8* 7* 6)/(5* 4* 3* 2)\\\\i.e.\\\\{10}_C_5=252`