4 Choose 2

Combination Calculator
Total items (n)
Items chosen (k)

What is 4 choose 2?

Answer

4 choose 2 is
6

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

C(4, 2) = 4! / (2! · 2!)

= (4 × 3) / (2 × 1)
= 12 / 2

= 6

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

Row 4 of Pascal's triangle
k4 choose k
01
14
26
34
41

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

See Also

Recalculate with different values ↑

n choose 2 for other n

n choose 2Answer
1 choose 20
2 choose 21
3 choose 23
4 choose 26
5 choose 210
6 choose 215
7 choose 221
8 choose 228
9 choose 236
10 choose 245
11 choose 255
12 choose 266
13 choose 278
14 choose 291
15 choose 2105

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)!.

See Also