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6 May, 09:03

A die is rolled 10 times. What is the probability that 1, 2 and 3 occur once each, 4 and 5 occur twice each, and 6 occurs 3 times?

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  1. 6 May, 09:19
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    Answer: 0.0025

    Step-by-step explanation:

    Given that 1,2,3 occur once each, 4 and 5 occur twice each, 6 occurs 3 times,

    A possible outcome we have is [1,2,3,4,4,5,5,6,6,6]

    Total number of ways to arrange this outcome is 10! Ways.

    Since 1 occurs once, number of ways we can arrange that just 1 is 1!

    Since 2 occurs once, number of ways we can arrange that just 2 is 1!

    Since 3 occurs once, number of ways we can arrange that just 3 is 1!

    Since 4 occurs twice, number of ways we can arrange that just 4 is 2

    Since 5 occurs twice, number of ways we can arrange that just 5 is 2!

    Since 6 occurs on thrice, number of ways we can arrange that just 6 is 3!

    Hence, total number of ways this our particular outcome can be arranged is 10! / (1! * 1! * 1! * 2! * 2! * 3!)

    =3628800/24

    =151200

    However, the total number of sample space for this die is 6^10 = 60466176

    Hence, the probability of 1, 2 and 3 occur once each, 4 and 5 occur twice each, and 6 occurs 3 times = 151200/60466176 = 0.0025
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