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

correct option is D. 54

Step-by-step 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