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The only way to produce 4 as a product of digits is to have either a '4'

or else '2 x 2' among the digits, and ' 1 ' for all the rest of them.

Possibilities that include a '4':

11114

11141

11411

14111

41111

. . . . . . . . . 5 possibilities

Possibilities that include a pair of 2s :

11122

11212

12112

21112

11221

12121

21121

12211

21211

22111

. . . . . . . . . 10 possibilities

Total = 5 + 10 = 15 possibilities

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Q: How many 5 digit number have digits whose product is equal to 4?
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