Question

How many ways can an IRS auditor select 5 of 12 tax returns for an audit?A. 120B. 248,832C. 95,040D. 792

Answer 1

Since order is not important, the combination may be used. The formula is as follows.

`_nC_r=(n!)/(r!(n-r)!)`

where n is the number of possible options and r is the number of chosen options.

Thus, the given are as follows.

`\begin{gathered} n=12 \\ r=5 \end{gathered}`

Substitute the given values into the formula and then simplify.

`\begin{gathered} _(12)C_5=(12!)/(5!(12-5)!) \\ =(12!)/(5!(7)!) \\ =((12)(11)(10)(9)(8)(7!))/((5!)(7!)) \\ =((12)(11)(10)(9)(8))/(120) \\ =(95040)/(120) \\ =792 \end{gathered}`

Therefore, there must be 792 ways.