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Answer :
Final answer:
The number of different signals that can be formed by running 7 flags (3 white, 2 red, 2 blue) up a pole, one above the other, is 420.
Explanation:
This question is about permutations and combinations in mathematics, specifically with repeated items. The formula to calculate permutations with repetition is n! / (n1! * n2! * ... * nk!), where n is the total number of items, and n1, n2, ... nk are the numbers of each type of item.
Here we have 7 flags in total, with 3 white, 2 red and 2 blue flags. So, we plug these numbers into the formula to get the answer:
7! / (3! * 2! * 2!) = 5,040 / (6 * 2 * 2) = 420.
Therefore, there can be 420 different signals formed by running these 7 flags up a pole, one above the other.
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Final answer:
To find the number of different signals that can be made from seven flags (three white, two red, and two blue), you apply the formula for permutations of a multiset. This yields 210 different possible signals.
Explanation:
The question involves counting the number of ways to arrange 7 flags on a pole, using three colours: white, red, and blue. We're given specific counts of each colour: three white flags, two red flags, and two blue flags. In other words, we need to consider permutations of 7 items where some items are identical.
This can be solved by using the formula for permutations of a multiset: n!/[(n1!)(n2!)(n3!)...], where n is the total number of items, and n1, n2, n3, etc, are the individual counts of each type of item. In this case, n = 7 (for the total number of flags), n1 = 3 (for the white flags), n2 = 2 (for the red flags), and n3 = 2 (for the blue flags).
So we have 7!/(3!2!2!) = 5,040/ 24 = 210. Therefore, there are 210 different signals that can be made.
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