Ximpledu

Combination (Math)

See how to solve a combination (nCr).
4 examples and their solutions.

Combination

Formula

r numbers nCr = n⋅(n - 1)⋅(n - 2)⋅ ...r!
Meaning: From n things,
pick r things.
(no arrangement)

Permutation
Factorial
nCr = nCn - r - [1]
nC1 = n - [2]
nC0 = nCn = 1 - [3]
[1]
From n things,
(number of ways to pick r things)
= (number of ways to leave (n - r) things)
[2]
From n things, pick 1 thing
→ n ways
[3]
From n things,
(number of ways to pick 0 things)
= (number of ways to leave n things)
→ Don't do anything.
→ 1 way

Example

7C3
Solution

Example

8C6
Solution

Example

5 cups, 6 spoons
Find the number of ways to choose 2 cups and 3 spoons.
Solution

Example

3 letters: a, b, c
4 numbers: 1, 2, 3, 4
Find the number of ways to choose 2 letters and 2 numbers
and arrange them in a row.
Solution