Answer:
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
