Chapter 0, Problem 17PO

To determine

To calculate: Situation involves permutations and combinations.

Answer to Problem 17PO

Yes, it involves permutations and combinations.

There are 6435 ways to form a team.

Explanation of Solution

Given information:

Total number of athletes, n = 15.

Members in a team, r = 7

Used formula:

Permutation and combination is given by-

  $\frac{n!}{(n-r)!\times r!}$

Calculation:

Using the formula for permutations and combinations,

Permutations= $\frac{n!}{(n-r)!\times r!}$

Putting the values, we get −

  $\begin{array}{l}=\frac{15!}{(15-7)!\times 7!}\\ =\frac{15!}{8!\times 7!}\\ =\frac{15\times 14\times 13\times 12\times 11\times 10\times 9\times 8!}{8!\times 7\times 6\times 5\times 4\times 3\times 2\times 1}\\ =13\times 11\times 5\times 9\\ =6435\end{array}$

So, there are 6435 ways to form a team of 7.