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21 September, 18:07

A zealous geologist is sponsoring a contest in which entrants have to guess the age of a shiny rock. He offers these clues: the age of the rock is formed from the six digits 2, 2, 2, 3, 7, and 9, and the rock's age begins with an odd digit. How many possibilities are there for the rock's age

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  1. 21 September, 21:52
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    The total number of possibilities are 60.

    Step-by-step explanation:

    Given:

    There are 6 digits and 3,7,9 are odd ones.

    To Find:

    How many possibilities are there for the rock's age

    Solution:

    Here condition is that number should start with odd digit

    so there 3 number only as odd (3,7,9)

    So it leaves 3 repeating numbers i. e. 2

    So permutation of 5 numbers with 3 odd numbers

    So possible arrangement will be

    nPr

    n=5, r=3

    So 5P3=5!/3!

    And finally for all possibilities as

    =3 * (5!/3!)

    =3 * (20)

    =60
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