contestada

A committee of four is being formed randomly from the employees at a school: 5 administrators, 37 teachers, and 4 staff.How many ways can the committee be formed?

A committee of four is being formed randomly from the employees at a school 5 administrators 37 teachers and 4 staffHow many ways can the committee be formed class=

Respuesta :

Let us sum all the members of the committee

[tex]5+37+4=46[/tex]

Therefore, the number of ways committee of 4 can be formed from 46employees will be

[tex]^{46}C_4[/tex]

The formula for combination is,

[tex]C\left(n,r\right)=\lparen_r^n)^=\frac{n!}{(r!(n-r)!)}[/tex]

Given:

[tex]n=46,r=4[/tex]

Therefore,

[tex]C\left(n,r\right)=C\left(46,4\right)=\frac{46!}{(4!(46-4)!)}=\frac{46!}{4!×42!}=163185[/tex]

Hence, the answer is 163185ways.