Permutation and Combination
- Formula / Rule
- Permutation and Combination
- Topic
- Arithmetic
- Formula
Permutation (order matters): $${nPr = \frac{n!}{(n-r)!}}$$
Combination (order does not matter): $${nCr = \frac{n!}{r! \times (n-r)!}}$$
Factorial: $${n! = n \times (n-1) \times (n-2) \times \ldots \times 1}$$ $${0! = 1}$$
Key Identities:
- $nC0 = nCn = 1$
- $nCr = nC(n-r)$
- $nCr + nC(r-1) = (n+1)Cr$
- When to Use
- Counting arrangements, selecting groups, probability problems.
- Worked Example
Q: In how many ways can 4 persons sit in a row of 6 chairs?
$6P4 = \frac{6!}{(6-4)!} = \frac{6!}{2!} = \frac{720}{2} = \textbf{360 ways}$