Question

From a group of 15 women and 16 men, a researcher wants to randomly select 8 women and 8 men for a study. In how many ways can the study group be selected?A. 300,540,195B. 778,377,600C. 19,305OD. 82,818,450

Answer 1

Since we are talking about a group of people the order is not going to matter when we select the different people, then, start to make the combination for the group of women and the group of men separately.

`\begin{gathered} women=15C8 \\ women=(15!)/((15-8)!8!) \\ women=(15\cdot14\cdot13\cdot12\cdot11\cdot10\cdot9)/(7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1) \\ women=6435 \end{gathered}`
`\begin{gathered} men=16C8 \\ men=(16!)/((16-8)!8!) \\ men=(16\cdot15\cdot14\cdot13\cdot12\cdot11\cdot10\cdot9)/(8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1) \\ men=12870 \end{gathered}`

then, multiply the results

`\begin{gathered} 16C8\cdot15C8 \\ 12870\cdot6435 \\ 82,818,450 \end{gathered}`