IKMC 2027 - Grades 5-6 - Self-study SET 4 - Thematic Batch 3 Question 22

How many five-digit positive integers use 1, 2, 3, 4, 5 exactly once and have their first 2 digits divisible by 2, first 3 by 3, first 4 by 4, and the entire number divisible by 5?