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If you are not allowed to repeat the digits then the answer is clearly 0.

If you are allowed to repeat digits then the only way you can possibly reach a product of 4 is by using a combination of 3 "1's" and 2 "2's". The possible combinations are therefore:

22111

21211

21121

21112

12211

12121

12112

11221

11212

11122

Thus there are 10 numbers which meet the criteria.

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Q: How many 5 digit numbers from 1 0 6 2 9 and 7 have digits whose product is equal to 4?
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How many 5-digit numbers have digits whose product is equal to 4?

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