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6 Choose 3

Combination Calculator

What is 6 choose 3?

Answer

6 choose 3 is

20

Order doesn't matter, no repeats: 20 ways to choose 3 of 6 items.

C(6, 3) = 6! / (3! · 3!)

= 20

If order matters (permutations): P(6, 3) = 6 × 5 × 4 = 120 — each combination in 3! = 6 orders.

Row 6 of Pascal's triangle
k	6 choose k
0	1
1	6
2	15
3	20
4	15
5	6
6	1

Row sum: 2⁶ = 64 — all subsets of 6 items.

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https://calculat.io/en/number/combinations/6--3

<a href="https://calculat.io/en/number/combinations/6--3">6 Choose 3: Combinations C(6, 3) - Calculatio</a>

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6 Choose 3: Combinations C(6, 3). 6 choose 3 = 20: the number of ways to choose 3 of 6 items when order doesn't matter and nothing repeats. C(6, 3) = (6 × 5 × 4) / (3 × 2 × 1).

https://calculat.io/en/number/combinations/6--3/generated.jpg

n choose 3 for other n

n choose 3	Answer
1 choose 3	0
2 choose 3	0
3 choose 3	1
4 choose 3	4
5 choose 3	10
6 choose 3	20
7 choose 3	35
8 choose 3	56
9 choose 3	84
10 choose 3	120
11 choose 3	165
12 choose 3	220
13 choose 3	286
14 choose 3	364
15 choose 3	455

Recalculate with different values ↑

FAQ

What is 6 choose 3?

6 choose 3 is 20

Why is 6 choose 3 the largest number in row 6?

In row 6 of Pascal's triangle the numbers grow towards the middle and shrink after it, because n choose k = n choose (n − k). With an even n the middle is k = 3, so 6 choose 3 = 20 is the largest: 6 choose 2 is only 15.

How many ways are there if order matters?

P(6, 3) = 120. Each of the 20 combinations can be put in order in 3! = 6 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.