Question

There are 20 members of a basketball team.

Answer 1

Answer:

a)125970

b)95040

c)35640

Step-by-step explanation:

a) selecting 12 player from 20 players can be one in $^{20} C_{12}$

 $^{20} C_{12}$ = $\frac{20!}{12!X (20-12)!}$

          =  $\frac{20!}{12!X8!}$

          = $125970$

b) since each position has an identity permutations can be used so

   Number of ways = $^{12} P_{5}$

                                = $\frac{12!}{(12-5)!}$

                                = $\frac{12!}{7!}$

                                = $95040$

c) coach permutes 4 players for position other than centers in  $^{12}P_{4}$ ways and selects center in 3 ways

  so, number of ways = $^{12}P_{4}X3$

                                     =$\frac{12!}{8!}X3$

                                     =$35640$