4 Choose 2

Combination Calculator

What is 4 choose 2?

Answer

4 choose 2 is

Order doesn't matter, no repeats: 6 ways to choose 2 of 4 items.

C(4, 2) = 4! / (2! · 2!)

= 6

If order matters (permutations): P(4, 2) = 4 × 3 = 12 — each combination in 2! = 2 orders.

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

Row sum: 2⁴ = 16 — all subsets of 4 items.

Found an error in the calculation or the information?

n choose 2 for other n

n choose 2	Answer
1 choose 2	0
2 choose 2	1
3 choose 2	3
4 choose 2	6
5 choose 2	10
6 choose 2	15
7 choose 2	21
8 choose 2	28
9 choose 2	36
10 choose 2	45
11 choose 2	55
12 choose 2	66
13 choose 2	78
14 choose 2	91
15 choose 2	105

Recalculate with different values ↑

FAQ

What is 4 choose 2?

4 choose 2 is 6

Why is 4 choose 2 the largest number in row 4?

In row 4 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 = 2, so 4 choose 2 = 6 is the largest: 4 choose 1 is only 4.

How many ways are there if order matters?

P(4, 2) = 12. Each of the 6 combinations can be put in order in 2! = 2 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

4 Choose 2

What is 4 choose 2?

See Also

n choose 2 for other n

FAQ

What is 4 choose 2?

Why is 4 choose 2 the largest number in row 4?

How many ways are there if order matters?

See Also