Recognise the difference between permutations and combinations and know when each should be used

What are Permutations? 🔄

Permutations are arrangements of items where the order matters. Think of lining up your favourite books on a shelf: putting the red book first and the blue book second is different from swapping them.

Formula: $nP_r = \dfrac{n!}{(n-r)!}$

What are Combinations? 📚

Combinations are selections of items where the order does not matter. Imagine picking 3 books to bring to school: choosing books A, B, C is the same as choosing C, B, A.

Formula: $nC_r = \dfrac{n!}{r!(n-r)!}$

When to Use Which? 🤔

• Permutations when you need to count different arrangements or sequences.
• Combinations when you need to count different groups or selections.

Quick check: Does the order change the outcome? If yes → permutations; if no → combinations.

Examples & Analogy 🎲

1. Permutations Example: Arrange 3 out of 5 different coloured marbles in a row.
   • Number of ways: $5P_3 = \dfrac{5!}{(5-3)!} = 60$
   • Why? Because putting the red marble first and the blue second is different from the reverse.
2. Combinations Example: Choose 3 out of 5 different coloured marbles to take on a trip.
   • Number of ways: $5C_3 = \dfrac{5!}{3!(5-3)!} = 10$
   • Why? Because the order you pick them in doesn't matter.

Exam Tips for IGCSE 0606 📝

• Always read the question carefully: “arrange” vs “select”.
• Use the correct formula: $nP_r$ for arrangements, $nC_r$ for selections.
• Check for factorials: remember that $n! = n \times (n-1) \times \dots \times 1$.
• When in doubt, write a short example on scratch paper to see if order matters.
• Practice with small numbers first to build confidence before tackling larger values.