Question

How many positive integers less than 10,000 are such that the product of their digits is 210?A. 24

B. 30
C. 48
D. 54
E. 72

Answer 1

correct option is D. 54

Explanation:

given data

product of digits = 210

integers = 10000

to find out

How many positive integers less than 10,000

solution

we know product of digits 210 are = 1 × 2× 3×5×7

210 = 1 × 6 × 5 × 7

here 2 × 3 = 6 ( only single digit )

here 4 digit numbers with combinations of the digits are = {1,6,5,7} and {2,3,5,7}

3 digit numbers with combinations of digits are = {6,5,7}

and product of their digits = 210

so combination will be

combinations of {1,6,5,7} is 4! = 4 × 3 × 2 × 1 = 24

combinations of {2,3,5,7} is 4! = 4 × 3 × 2 × 1 = 24

combinations of {6,5,7} is 3! = 3 × 2 × 1 = 6

so total is = 24 + 24 + 6

total is = 54

so correct option is D. 54