CAT 2022 Slot 2 QA Question 19: The number of integers greater than 2000 that can be formed with the digits 0, 1, 2, 3, 4, 5, using each digit at most once, is

Question

The number of integers greater than 2000 that can be formed with the digits 0, 1, 2, 3, 4, 5, using each digit at most once, is

Accepted Answer

Only 4-digit, 5-digit and 6-digit numbers can be greater than 2000.

For 4-digit numbers, the first digit can be 2, 3, 4 or 5.

$	ext{Number of 4-digit numbers} = 4 	imes 5 	imes 4 	imes 3 = 240$

For 5-digit numbers, the first digit cannot be 0.

$	ext{Number of 5-digit numbers} = 5 	imes 5 \