Question

A planning committee for a project must consist of six members. There are 8 architects and 5 engineers. In how many different ways can this planning committee be formed?

Answer 1

Since there are no restrictions for members' occupation, we just need to chose 6 members out of 13 people. We can do this in

$\displaystyle C(13,6)=\begin{pmatrix} 13 \\6 \end{pmatrix} = \frac{13!}{6!\,7!} = \frac{13 \cdot 12 \cdot 11 \cdot10 \cdot 9 \cdot8}{6 \cdot5\cdot4\cdot3\cdot2\cdot1} =1716$ different ways.

Answer: 1716 ways.