Question

The principal would like to assemble a committee of 11 students from the the 19 member student council. How many different committees can be chosen?

Answer 1

Answer: 75582 different committees

Step-by-step explanation

Given

• Committee: 11 students

,

• Member student council: 19 students

Procedure

As the order of choosing is not important, then we can use combinations:

`_nC_r=(n!)/((n-r)!r!)`

where n is the number of items in a set and r is the number of items selected from the set. Applying the formula to our problem:

• n = ,19

,

• r = 11

Thus, replacing these values and simplifying:

`_(19)C_(11)=(19!)/((19-11)!11!)`
`_(19)C_(11)=(19!)/((8)!11!)`
`_(19)C_(11)=(19!)/(8!\cdot11!)`
`_(19)C_(11)=75582`