The bigger digits

Probability Level pending

How many numbers of three digits distinct and different from zero there, such that the digit of tens is bigger than the other?


The answer is 168.

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1 solution

Zee Ell
Sep 12, 2016

We can choose the 3 distinct digits out of the 9 digits allowed (1, 2, ..., 8, 9):

( 9 3 ) = 84 ways. { 9 \choose 3 } = 84 \text { ways. }

Since we have to put the largest digit in the middle and we can arrange the remaining 2 digits in 2! = 2 ways, therefore our answer should be:

84 × 2 = 168 84 × 2 = \boxed {168}

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