Chapter 8, Problem 24CT

To determine

To calculate:

The probability value for the random selection of the six teams

Answer to Problem 24CT

The probability value for the random selection of the six teams from the Big Ten Conference is $\frac{1}{924}$ .

Explanation of Solution

Given information:

Team of basketball: $12$ men’s

Calculation:

Consider,

Six men’s participated in the NCAA Men’s Basketball Championship Tournament from total twelve men’s of basketball teams in the Big Ten Conference.

The six teams participated in Conference by $C{}_1$ ways. Now, the random selection of these six teams from the Big Ten Conference is given as:

  $S=C{}_6\times C{}_1$

Need to find the probability value for the random selection of six teams from the Big Ten Conference which should be same as probability values the six teams that participated in the tournament:

  $\begin{array}{l}P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}\\ P\left(E\right)=\frac{C{}_1}{C{}_6\times C{}_1}\\ P\left(E\right)=\frac{1}{C{}_6}\\ P\left(E\right)=\frac{\left(12-6\right)!6!}{12!}\left[\because C{}_r=\frac{n!}{\left(n-r\right)!r!}\right]\\ P\left(E\right)=\frac{6!6!}{12!}\\ P\left(E\right)=\frac{1}{924}\end{array}$