Question

How many ways can a coach choose the 3 starting players from a volleyball team of 7

Answer 1

This is combination

number of ways of choosing 3 players from 7 players

`=^nC_r^{}`

n = 7 and r = 3

`=^nC_r\text{ = }(n!)/((n-r)!r!)`
`\begin{gathered} =\text{ }(7!)/((7-3)!3!) \\ =\text{ }(7!)/(4!3!) \end{gathered}`
`\begin{gathered} =\text{ }(7X6X5X4X3X2X1)/(4X3X2X1X3X2X1) \\ =\text{ }(5040)/(144) \end{gathered}`

= 35 ways