Question

19. There are 24 students in an MA 206 class at FCC. How many ways are there to select 5 students for a group project?

Answer 1

Given,

The number of students are 24.

The number of students to be selected is 5.

The number of ways to select 5 students for a group project is,

`^nC_r=(n!)/(r!(n-r)!)`

Here, n is the number of total students.

r is the number of students get selected.

Substituting the values then,

`\begin{gathered} ^(24)C_5=(24!)/(5!(24-5)!) \\ =(24!)/(5!*19!) \\ =(24*23*22*21*20*19!)/(5*4*3*2*1*19!) \\ =(5100480)/(120) \\ =42,504 \end{gathered}`

Hence, the number of ways to select 5 students for a group project is 42504.