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
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[tex]C_{8}[/tex].
⇒ 18[tex]C_{8}[/tex] = [tex]\frac{18!}{(18 - 8)!8!}[/tex]
= [tex]\frac{18!}{10!8!}[/tex]
= [tex]\frac{18*17*16*15*14*13*12*10*9*8!}{10*9*8*7*6*5*4*3*2*1*8!}[/tex]
= [tex]\frac{18*17*16*15*14*13*12*11*10*9}{10*9*8*7*6*5*4*3*2}[/tex]
= [tex]\frac{158789030400}{3628800}[/tex]
= 43758
The number of swimmer squad the could be selected by the coach is 43758.
