Chapter 13, Problem 2MCQ

To determine

To calculate:

Number of different signals can be made with $5$ flags from $8$ flags of different colors.

Answer to Problem 2MCQ

Number of different signals can be made with $5$ flags from $8$ flags of different colors is $6720$ .

Explanation of Solution

Given information:

Number of flags: $5$ from $8$ flags of different colors.

Calculations:

The number of ways that $5$ flags can be selected is the combination of $8$ flags taken $5$ at a time.

After selecting $5$ flags from $8$ , it can be arranged in $P{}_5$ ways.

Therefore, total number of signals that can be made is,

  $\begin{array}{l}C{}_5\left(P{}_5\right)\\ =\left(\frac{8!}{\left(8-5\right)!\left(5\right)!}\right)\left(5!\right)\\ =6720\end{array}$

Thus, Number of different signals can be made with $5$ flags from $8$ flags of different colors is $6720$ .