High School

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How many distinct flags can be made from 8 flags hung in a vertical line, consisting of 4 distinct red flags, 3 distinct white flags, and one blue flag?

Answer :

Final answer:

To find the number of distinct flags possible with 4 red flags, 3 white flags, and 1 blue flag hung in a line, we calculate the permutations and account for repetitions due to identical flags. The result is 280 distinct arrangements.

Explanation:

To calculate the number of distinct flags that can be made from 8 flags hung in a vertical line, consisting of 4 distinct red flags, 3 distinct white flags, and one blue flag, we use the concept of permutations. The total number of ways to arrange 8 flags is given by 8!. However, since we have flags of the same color that are distinct, we divide this by the factorial of the number of identical flags to account for repetitions.

So the formula we use is:

(Total permutations) = (Total number of flags)! / (Red flags)! / (White flags)! / (Blue flags)!

Plugging in the values we get:

(Total permutations) = 8! / 4! / 3! / 1! = (40320) / (24*6*1) = 40320 / 144 = 280

Therefore, there are 280 distinct flags that can be made.

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