Question

Evaluate 9c3 and 12p3

Answer 1

We need the formulas for combinations and permutations

`\begin{gathered} \text{nCk}=(n!)/(k!(n-k)!) \\ \text{nPk}=(n!)/((n-k)!) \end{gathered}`

Replacing the information we have

`\begin{gathered} 9C3=(9!)/(3!(9-3)!)=(9!)/(3!6!)=84 \\ 12P3=(12!)/((12-3)!)=(12!)/(9!)=1320 \end{gathered}`

Then 9C3=84 and 12P3=1320.