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

Answer:

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

Step-by-step 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$C_{8}$ = $\frac{18!}{(18 - 8)!8!}$

                                       = $\frac{18!}{10!8!}$

                                       = $\frac{18*17*16*15*14*13*12*10*9*8!}{10*9*8*7*6*5*4*3*2*1*8!}$

                                       = $\frac{18*17*16*15*14*13*12*11*10*9}{10*9*8*7*6*5*4*3*2}$

                                       = $\frac{158789030400}{3628800}$  

                                       = 43758

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

                   

Answer 2

Answer:

43,758 different swimmer squad

Step-by-step 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