Chapter 13.9, Problem 9PPS

To determine

To calculate: No. of schedules can be made.

Answer to Problem 9PPS

Thus, No. of schedules can be possible to made is $10$ .

Explanation of Solution

Given information:

Chess team wants to have practice two different days next week from Monday to Friday.

Calculation:

A combination is an arrangement, so order is not a significant thing.

Whereas selecting the days of practice session, order is important.

So combination is used.

Thus, number of combinations,

  $=\frac{Thenumberofpermutations}{Thenumberofways}$

Total number of days from Monday to Friday are $5$ .

There are $5$ random choices for the first day, $4$ choices for the second day.

Number of permutations,

  $\begin{array}{l}=5\times 4\\ =20\end{array}$

There are $2-1$ ways to practice for two different days.

Thus, number of combinations as below:

  $\begin{array}{l}C\left(10,2\right)=\frac{20}{2}\\ =10\end{array}$