NIMCET 2019 Question Paper with solutions

Prime factorization of $210=2\times 3\times 5\times 7$
So. four digit numbers with combinations of the digits |1. 6, 5. 7} and {2, 3, 5, 7} and three digit numbers with combinations of digits {6, 5, 7} will have the product of their digits equal to 210.
Combination of four digits {1, 6, 5, 7} $=4!=4\times 3\times 2\times 1=24$
Combination of four digits {2, 3, 5, 7}$=4!=4\times 3\times 2\times 1=24$
Combination of three digits {6, 5, 7} $=3!=3\times 2\times 1=6$
Hence, total combinations $=24+24+6=54$