11 Choose 4

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

What is 11 choose 4?

Answer

11 choose 4 is
330

Order doesn't matter, no repeats: 330 ways to choose 4 of 11 items.

C(11, 4) = 11! / (4! · 7!)

= (11 × 10 × 9 × 8) / (4 × 3 × 2 × 1)
= 7,920 / 24

= 330

If order matters (permutations): P(11, 4) = 11 × 10 × 9 × 8 = 7,920 — each combination in 4! = 24 orders.

Row 11 of Pascal's triangle
k11 choose k
01
111
255
3165
4330
5462
6462
7330
8165
955
1011
111

Row sum: 211 = 2,048 — all subsets of 11 items.

See Also

Recalculate with different values ↑

n choose 4 for other n

n choose 4Answer
4 choose 41
5 choose 45
6 choose 415
7 choose 435
8 choose 470
9 choose 4126
10 choose 4210
11 choose 4330
12 choose 4495
13 choose 4715
14 choose 41,001
15 choose 41,365
16 choose 41,820
17 choose 42,380
18 choose 43,060

FAQ

What is 11 choose 4?

11 choose 4 is 330

Why is 11 choose 4 the same as 11 choose 7?

Every way to choose 4 of 11 items leaves exactly 7 behind, so choosing 4 and choosing which 7 to leave out are the same count: 11 choose 4 = 11 choose 7 = 330. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(11, 4) = 7,920. Each of the 330 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also