Question

1. 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) $\frac{1}{2,220,075}$
b) $\frac{1}{40,320}$
c) $\frac{1}{213,127,200}$
d) $\frac{8}{27}$

Explanation:

Step1: Calculate the number of combinations

The number of ways to choose 8 players out of 27 is given by the combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n = 27$ and $r=8$. So $C(27,8)=\frac{27!}{8!(27 - 8)!}=\frac{27!}{8!×19!}=\frac{27\times26\times25\times24\times23\times22\times21\times20}{8\times7\times6\times5\times4\times3\times2\times1}=2220075$.

Step2: Determine the favorable - outcome

There is only 1 way to select the 8 tallest players.

Step3: Calculate the probability

The probability $P$ of an event is the number of favorable outcomes divided by the number of total outcomes. So $P=\frac{1}{2220075}$.

Answer:

A. $\frac{1}{2,220,075}$