CAT 2020 Slot 2 QA Question 10: How many 4-digit numbers, each greater than 1000 and each having all four digits distinct, are there with 7 coming before 3?

Question

How many 4-digit numbers, each greater than 1000 and each having all four digits distinct, are there with 7 coming before 3?

Accepted Answer

The number must contain both $7$ and $3$, and $7$ must appear before $3$.

Choose the other two digits from the $8$ digits other than $7$ and $3$.

Case 1: Neither of the two extra digits is $0$.
${}^{7}C_2 = 21$
For each such selection, half of the $4!$ arrangements have $7$ before $3$.
$21 	imes