JEE · Maths · Permutations &amp; Combinations doubts

What does “Permutation” actually mean in Permutations & Combinations, and why does it matter for JEE?

an arrangement where order matters: nPr = n!/(n−r)!.

I keep getting “Permutation” questions wrong in Permutations & Combinations. What's the trap?

using permutations when order doesn't matter.

What does “Combination” actually mean in Permutations & Combinations, and why does it matter for JEE?

a selection where order does not matter: nCr = n!/[r!(n−r)!].

I keep getting “Combination” questions wrong in Permutations & Combinations. What's the trap?

using combinations when order actually matters.

What does “Fundamental principle of counting” actually mean in Permutations & Combinations, and why does it matter for JEE?

if one task has m ways and another n ways, together they have m×n ways.

I keep getting “Fundamental principle of counting” questions wrong in Permutations & Combinations. What's the trap?

adding when you should multiply independent choices.

What is the difference between permutation and combination?

A permutation counts ordered arrangements (a password); a combination counts unordered selections (a team) — nCr = nPr / r!.

What is the difference between with repetition and without repetition?

With repetition, items can be reused (like digits in a PIN); without repetition, each item is used at most once (like ranking people).

When do I use nPr = n!/(n−r)! in Permutations & Combinations, and what does it mean?

number of ordered arrangements of r from n.

When do I use nCr = n!/[r!(n−r)!] in Permutations & Combinations, and what does it mean?

number of unordered selections of r from n.

How is Permutations & Combinations tested in JEE, and what should I focus on?

Prioritise the core ideas: Permutation, Combination, Fundamental principle of counting.

What are the most common mistakes students make in Permutations & Combinations?

if rearranging the same items doesn't create a new outcome, use combinations, not permutations.

How do I revise Permutations & Combinations quickly before the exam?

One-page summary of Permutation, Combination, Fundamental principle of counting, then timed previous-year questions.