Use counting rules to determine the probability.
-8 basketball players are to be selected to play in a special game. The players will be selected from a list of 27 players. If the players are selected randomly, what is the probability that the 8 tallest Players will be selected?
A) $\frac { 8 } { 27 }$
B) $\frac { 1 } { 2,220,075 }$
C) $\frac { 1 } { 213,127,200 }$
D) $\frac { 1 } { 40,320 }$

Question

Use counting rules to determine the probability.
-8 basketball players are to be selected to play in a special game. The players will be selected from a list of 27 players. If the players are selected randomly, what is the probability that the 8 tallest Players will be selected? 
A) $\frac { 8 } { 27 }$
B) $\frac { 1 } { 2,220,075 }$
C) $\frac { 1 } { 213,127,200 }$
D) $\frac { 1 } { 40,320 }$

Quizplus · Accepted Answer

The probability is calculated by dividing the number of ways to choose the 8 tallest players (which is 1 way, since there's only one group of the 8 tallest) by the total number of ways to choose any 8 players from 27, which is calculated using the combination formula $C(n, k) = \frac{n!}{k!(n-k)!}$. Therefore, the probability is $\frac{1}{C(27, 8)} = \frac{1}{2,220,075}$.

Use Counting Rules to Determine the Probability 827\frac { 8 } { 27 }278​

Use Counting Rules to Determine the Probability $\frac { 8 } { 27 }$