Calvin thinks of a 5-digit number. The product of the digits is 200.
How many different numbers which Calvin could have thought of?
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We note that 2 0 0 = 2 3 × 5 2 . There are only 3 possible combinations and the respective permutations are as follows:
Combination 1 1 5 5 8 1 2 4 5 5 2 2 2 5 5 ⇒ ⇒ ⇒ Permutations 2 ! × 2 ! 5 ! = 4 1 2 0 2 ! 5 ! = 2 1 2 0 2 ! × 3 ! 5 ! = 1 2 1 2 0 Total: = 3 0 = 6 0 = 1 0 1 0 0
The total number of such 5-digit numbers is 1 0 0 .