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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 7 flags will be flown.

Find the number of different signals consisting of 7 flags if the first flag must be yellow.

If the first flag is yellow, then the number of different signals consisting of 7 flags is _____________.

Answer :

Final answer:

The number of different signals consisting of 7 flags with the first flag being yellow is 48,048.

Explanation:

To find the number of different signals consisting of 7 flags, with the first flag being yellow, we need to consider the combination of colors for the remaining 6 flags. Since there are 15 different colored flags to choose from, we have 14 options for the second flag, 13 options for the third flag, and so on, until we have 8 options for the seventh flag.

Therefore, the number of different signals is calculated as 14 * 13 * 12 * 11 * 10 * 9 * 8 = 48,048.

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