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The product of all digits of positive integer M is 105 How many such Ms are there with distinct digits?

 Mar 29, 2021
 #1
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105=3*5*7

total : 3!=3*2*1=6

 Mar 29, 2021
 #2
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M can include a 1 as well.

The number of Ms that include a 1 is equal to 4! = 24, so the final answer is 6+24=30

textot  Mar 29, 2021

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