Chapter 13.9, Problem 10PPS

To determine

To calculate: No. of ways can students choose three colors for the flag.

Answer to Problem 10PPS

No. of ways can students choose three colors for the flag is $10$ .

Explanation of Solution

Given information:

Colors of a new school flag: blue, white, red, black and gold.

Calculation:

Total number of colors is $5$ .

Whereas the selecting the colors for the flag, order is not important.

So combination will be used.

There are five choices for selecting the first color,

  $4$ choices for selecting the second color,

  $3$ choices for the third color.

So number of permutations,

  $\begin{array}{l}=5\times 4\times 3\\ =60\end{array}$

There are $3\times 2\times 1$ ways the student can choose $3$ colors for the flag.

The number of combination the students can choose $3$ colors for the flag are as below:

  $\begin{array}{l}C\left(5,3\right)=\frac{60}{3\times 2\times 1}\\ =\frac{60}{6}\\ =10\end{array}$