Question

Product of the distinct digits of a natural number is 60. How many such numbers are possible?

Answer 1

Possible 3 digits number such that product of distinct digits of a natural number is 60 :- 265,345
Each of the digit can be arranged in 3!. so, 2*3! = 12
Possible 3 digits number such that product of distinct digits of a natural number is 60 :- 1265,1345
Each of the digit can be arranged in 4!. so, 2*4! = 48
Total such numbers =12 + 48 = 60.