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11 Choose 10

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What is 11 choose 10?

Answer

11 choose 10 is

11

Order doesn't matter, no repeats: 11 ways to choose 10 of 11 items.

Choosing 10 of 11 is the same as leaving 1 out: C(11, 10) = C(11, 1).

C(11, 10) = 11! / (10! · 1!)

= C(11, 1)

= 11

If order matters (permutations): P(11, 10) = 11 × 10 × 9 × … × 2 = 39,916,800 — each combination in 10! = 3,628,800 orders.

Row 11 of Pascal's triangle
k	11 choose k
0	1
1	11
2	55
3	165
4	330
5	462
6	462
7	330
8	165
9	55
10	11
11	1

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

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https://calculat.io/en/number/combinations/11--10

<a href="https://calculat.io/en/number/combinations/11--10">11 Choose 10: Combinations C(11, 10) - Calculatio</a>

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11 Choose 10: Combinations C(11, 10). 11 choose 10 = 11: the number of ways to choose 10 of 11 items when order doesn't matter and nothing repeats. C(11, 10) = 11 / 1.

https://calculat.io/en/number/combinations/11--10/generated.jpg

n choose 10 for other n

n choose 10	Answer
2 choose 10	0
10 choose 10	1
11 choose 10	11
12 choose 10	66
13 choose 10	286
14 choose 10	1,001
15 choose 10	3,003
16 choose 10	8,008
17 choose 10	19,448
18 choose 10	43,758
19 choose 10	92,378
20 choose 10	184,756
100 choose 10	17,310,309,456,440

Recalculate with different values ↑

FAQ

What is 11 choose 10?

11 choose 10 is 11

Why is 11 choose 10 the same as 11 choose 1?

Every way to choose 10 of 11 items leaves exactly 1 behind, so choosing 10 and choosing which one to leave out are the same count: 11 choose 10 = 11 choose 1 = 11. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(11, 10) = 39,916,800. Each of the 11 combinations can be put in order in 10! = 3,628,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.