Question

Simplify 9c4A. 126B. 15,120C. 5D. 3,024

Answer 1

The given combination is:

`_9C_4`

Combinations are given by the following formula:

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

Where n is the size of the set and r is the subset size. In this case, n=9 and r=4, let's replace these values and solve:

`\begin{gathered} _9C_4=(9!)/(4!(9-4)!) \\ _9C_4=(9!)/(4!*5!) \\ \\ _9C_4=(362880)/(24*120) \\ \\ _9C_4=(362880)/(2880) \\ \\ _9C_4=126 \end{gathered}`

The answer is A. 126