Question

In selecting players from a Virginia soccer team of 10 players to form a national team, how many different possibilities exist for the national team?

(A) 1024
(B) 100
(C) 1
(D) 45

Answer 1

The number of different possibilities for selecting players from a Virginia soccer team of 10 players to form a national team is 252.

Step-by-step explanation:

The question asks how many different possibilities exist for selecting players from a Virginia soccer team of 10 players to form a national team. This is a combinatorial problem known as a combination. To find the number of combinations, we use the formula nCr = n! / (r!(n-r)!), where n is the total number of players and r is the number of players we want to select. In this case, n = 10 and r = 5, so the number of different possibilities for the national team is:

nCr = 10! / (5!(10-5)!) = 10! / (5!5!) = (10*9*8*7*6) / (5*4*3*2*1) = 252

Therefore, there are 252 different possibilities for the national team.