What is 5!?

120

5! = 5 × 4 × 3 × 2 × 1 = 120. Factorial means the product of all positive integers up to that number.

Understanding Combinatorics questions

Combinatorics questions ask how many arrangements or selections are possible. The whole decision comes down to one question: does order matter?

How to approach it

1. Decide whether order matters — permutation if yes, combination if no.
2. Apply nPr = n!/(n−r)! or nCr = n!/(r!(n−r)!).
3. Handle restrictions first, then arrange the remaining items.
4. Use the complement rule when "at least one" appears in the question.

Common mistakes to avoid

• Using a permutation where a combination is required.
• Double counting arrangements of identical items.
• Forgetting that 0! equals 1.

Where it appears: Standard in CBSE Class 11, IB HL and competitive aptitude tests.