Question

A signal can be sent from one location to another by running different colored flags up a flagpole, one above the other. There are 15 different colored flags to choose from but only 8 flags will be flown. Find the number of different signals consisting of 8, if the first flag must be blue.
If the first flag is blue then the number of different signals consisting of 8 flags is ??

Answer 1

Using the permutation formula, it is found that there are 17,297,280 different signals consisting of 8 flags.

In this problem, the order in which the flags are visited is important, hence the permutation formula is used to solve this question.

What is the permutation formula?

The number of possible permutations of x elements from a set of n elements is given by:

$P_{(n,x)} = \frac{n!}{(n-x)!}$

The first flag is blue, then the remaining 7 are taken from a set of 14, hence:

$P_{(14,7)} = \frac{14!}{7!} = 17,297,280$

There are 17,297,280 different signals consisting of 8 flags.

More can be learned about the permutation formula at brainly.com/question/25925367