Question

There are 18 athletes trying out for the olympic swimming team. The coach only has room for 8 swimmers on the team. How many different swimmer squads could the coach select

Answer 1

The number of swimmer squad the could be selected by the coach is 43758.

Explanation:

Number of athletes = 18.

Number of swimmers required = 8.

The number of swimmer squads that could be selected by the coach without repetition is 18
`C_(8)`.

⇒ 18
`C_(8)` =
`(18!)/((18 - 8)!8!)`

=
`(18!)/(10!8!)`

=
`(18*17*16*15*14*13*12*10*9*8!)/(10*9*8*7*6*5*4*3*2*1*8!)`

=
`(18*17*16*15*14*13*12*11*10*9)/(10*9*8*7*6*5*4*3*2)`

=
`(158789030400)/(3628800)`

= 43758

The number of swimmer squad the could be selected by the coach is 43758.

Answer 2

43,758 different swimmer squad

Explanation:

Given;

Total Number of athletes n = 18

Number of athletes needed to be selected r = 8

For this case, the coach need to select 8 players from a total of 18 athletes with no particular order. So, this is a combination case since the order of selection is not relevant.

The number of different swimmer squads the coach could select is;

S = nCr

nCr = n!/(r!×(n-r)!)

Substituting the values of n and r;

S = 18C8

S = 18!÷(8! × (18-8)!)

S = 18! ÷ (8!×10!)

S = 43,758

Therefore, he can select 43,758 possible different squads