Question

A team of 5 IT specialists is to be selected to attend a lecture from 16 IT specialists. In how

many different ways can the team be formed?
124
4368
480
2880

Answer 1

`16C5= (16!)/(5! (16-5)!)= (16!)/(5! 11!)= (16*15*14*13*12*11!)/(5! 11!)`

If we simplify we got:

`16C5 = (16*15*14*13*12)/(5*4*3*2*1)=4368`

And the best option would be:

4368

Explanation:

For this case we have a total of 16 IT specialists and we want to select 5 IT specialists from the total of 16 so we can use the combination formula given by:

`nC x= (n!)/(x! (n-x)!)`

And replacing we got:

`16C5= (16!)/(5! (16-5)!)= (16!)/(5! 11!)= (16*15*14*13*12*11!)/(5! 11!)`

If we simplify we got:

`16C5 = (16*15*14*13*12)/(5*4*3*2*1)=4368`

And the best option would be:

4368