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Answer :
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:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
The first flag is blue, then the remaining 7 are taken from a set of 14, hence:
[tex]P_{(14,7)} = \frac{14!}{7!} = 17,297,280[/tex]
There are 17,297,280 different signals consisting of 8 flags.
More can be learned about the permutation formula at https://brainly.com/question/25925367
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Final answer:
One can determine the number of different signal combinations starting with a blue flag by calculating the permutations of the remaining colors for the remaining slots, resulting in 3,364,720 possible combinations.
Explanation:
This problem can be solved by using the principle of permutations. Since the first flag is blue and we have 8 flag positions, we know only 7 positions are left to be filled with the remaining colored flags. As there are 14 color choices left from the available 15 (since one color, blue, is already in use), the problem becomes one of determining the permutations of 14 items taken 7 at a time.
The formula for permutations is: P(n, r) = n! / (n - r)!. Therefore, P(14, 7) = 14! / (14 - 7)!. When computing the factorial, we find there are 3,364,720 possible signals using these flags, with the first flag being blue.
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