Permutations & combinations
Counting arrangements and selections.
Learn with Kutty
Go one screen at a time. Press Next when you are ready. Tap 🔊 Read to me to listen.
To count choices, multiply the number of options at each step.
Look: Gold, silver and bronze from 5 runners: 5 choices, then 4, then 3.
✏️ Your turn!
Type your answer and press Check. Kutty will tell you if it is right.
14! = ?
25 people in a row: how many orders?
3Handshakes among 10 people?
! Careful!
✗Using arrangements for a team.
✓Teams have no order: divide by the repeats.
✗0! = 0.
✓0! = 1.
See the whole lesson on one page
To count choices, multiply the number of options at each step.
Arrangements (order matters): 1st, 2nd, 3rd place. Selections (order does not matter): picking a team. A selection counts each group once.
Think of it like this3 shirts and 2 pants make 3 × 2 = 6 different outfits.
- n!
- n × (n − 1) × … × 1. So 4! = 24.
Solved together
From 5 runners, how many ways can gold, silver and bronze be given? How many different teams of 3?
Medals: order matters. Fill each place.
5 × 4 × 3 = 60A team: order does not matter. Each team was counted 3 × 2 × 1 = 6 times in those 60.
60 ÷ 6 = 10
AnswerMedals: 60 ways. Teams: 10.
For older learners and grown-ups: a little more
ⁿPᵣ = n!/(n − r)! counts arrangements; ⁿCᵣ = n!/[r!(n − r)!] counts selections. Repeated letters: BANANA has 6!/(3! × 2!) = 60 arrangements.
Now practise it
Kanakku makes new questions on permutations & combinations every time. It shows the working and gives a hint when you are stuck.