11 Choose 5

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

What is 11 choose 5?

Answer

11 choose 5 is
462

Order doesn't matter, no repeats: 462 ways to choose 5 of 11 items.

C(11, 5) = 11! / (5! · 6!)

= (11 × 10 × 9 × 8 × 7) / (5 × 4 × 3 × 2 × 1)
= 55,440 / 120

= 462

If order matters (permutations): P(11, 5) = 11 × 10 × 9 × 8 × 7 = 55,440 — each combination in 5! = 120 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 5 for other n

n choose 5Answer
2 choose 50
5 choose 51
6 choose 56
7 choose 521
8 choose 556
9 choose 5126
10 choose 5252
11 choose 5462
12 choose 5792
13 choose 51,287
14 choose 52,002
15 choose 53,003
16 choose 54,368
17 choose 56,188
18 choose 58,568

FAQ

What is 11 choose 5?

11 choose 5 is 462

Why is 11 choose 5 the same as 11 choose 6?

Every way to choose 5 of 11 items leaves exactly 6 behind, so choosing 5 and choosing which 6 to leave out are the same count: 11 choose 5 = 11 choose 6 = 462. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(11, 5) = 55,440. Each of the 462 combinations can be put in order in 5! = 120 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also