Question

A signal can be formed by running different colored flags up a​ pole, one above the other. Find the number of different signals consisting of 10 flags that can be made using 4 white​ flags, 4 red​ flags, and 2 blue flags.

Answer 1

To find the number of different signals consisting of 10 flags using 4 white flags, 4 red flags, and 2 blue flags, you can use the concept of combinations. There are 210 different signals that can be made in this case.

Step-by-step explanation:

To find the number of different signals consisting of 10 flags using 4 white flags, 4 red flags, and 2 blue flags, you can use the concept of combinations. The formula to find combinations is given by:

C(n, r) = n! / (r!(n-r)!)

where n is the total number of flags and r is the number of flags of a particular color. Substituting the values, we get:

C(10, 4) x C(6, 4) x C(2, 2) = (10! / (4! x 6!)) x (6! / (4! x 2!)) x (2! / (2! x 0!)) = 210

Therefore, there are 210 different signals that can be made using 4 white flags, 4 red flags, and 2 blue flags.