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    Question

    How many different signals can be formed using 3 red, 2

    green, and 1 yellow flag?
    A 720 Correct Answer Incorrect Answer
    B 60 Correct Answer Incorrect Answer
    C 120 Correct Answer Incorrect Answer
    D 60 Correct Answer Incorrect Answer

    Solution

    We are given:

    • 3 red flags
    • 2 green flags
    • 1 yellow flag
    We are to find the number of different signals that can be formed using all these flags — where the order matters, but identical flags are indistinguishable. Total number of flags = 3 + 2 + 1 = 6 If all flags were distinct, the number of permutations = 6!=720 But since some flags are identical, we divide by factorials of repeated flags:
    • 3 red flags ⇒ divide by 3!
    • 2 green flags ⇒ divide by 2!
    • 1 yellow flag ⇒ no need (1! = 1)
    Total number of distinguishable signals:

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