Question

How many numbers with distinct digits are possible product of whose digits is 28

CAT 2021

CORRECT ANSWER WRONG ANSWER

CORRECT ANSWER WRONG ANSWER

CORRECT ANSWER WRONG ANSWER

CORRECT ANSWER WRONG ANSWER

Solution

Correct option is

(C)

Explanatory Answer :

We know that the prime factorisation of 28 is 2^2*7^1. That is 28=2*14=4*7.

Also, of course, anything multiplied by 1 is itself the number. (We have also 2*2*7 but [2,2,7] is not a list of distinct digits. )

So the only lists of distinct digits we can use are [4,7] and [1,4,7].

There are 2! permutations of [4,7]and 3! permutations of [1,4,7].

Thus we have counted 8 possibilities. (3*2 + 2)

hence , C is the correct option