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25 January, 09:31

A teacher has brought treats for her 10 students. She will give out 3 fruit snacks, 2 teddy grahams, and 5 granola bars. How many ways can she do this.

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  1. 25 January, 10:29
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    2520 ways

    Step-by-step explanation:

    We can solve this problem with 3 combinations:

    First the teacher needs to give 3 fruit snacks to 10 students, so we have a combination of 10 choose 3: C (10,3) = 10! / (3! * 7!) = 120

    Then, she needs to give 2 teddy grahams to 7 students (3 already got a snack), so a combination of 7 choose 2: C (7,2) = 7! / (2! * 5!) = 21

    The, she gives the 5 granola bars to the other 5 students, so a combination of 5 choose 5: C (5,5) = 1.

    Now we just need to multiply the combinations to find the result:

    C (10,3) * C (7,2) * C (5,5) = 120 * 21 * 1 = 2520 ways
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