Chapter SH, Problem 13.7MPS

To determine

Calculate number of possible ways of picking a team of 5 from 14 players for basketball team.

Answer to Problem 13.7MPS

There are 2002possible ways of picking a team of 5 from 14 players for basketball team.

Explanation of Solution

Given:

Total number of players, n = 14

Number of players to be selected, r = 5

Calculations:

Here, we have to calculate possible ways of picking a team of 5 from 14 players

A combination is nothing but selecting r number of objects from different n number of objects. Hence, it is an example of combination.

  $\begin{array}{l}{}^n{C}_r=\frac{n!}{r!}\\ {}^{14}{C}_5=\frac{14\times 13\times 12\times 11\times 10}{1\times 2\times 3\times 4\times 5}\\ {}^{14}{C}_5=7\times 13\times 11\times 2\\ {}^{14}{C}_5=2002\end{array}$

There are 2002possible ways of picking a team of 5 from 14 players.

Conclusion:

Therefore, we are able to calculate possible methods to select r numbers from given n numbers.