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11 Choose 8

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What is 11 choose 8?

Answer

11 choose 8 is

165

Order doesn't matter, no repeats: 165 ways to choose 8 of 11 items.

Choosing 8 of 11 is the same as leaving 3 out: C(11, 8) = C(11, 3).

C(11, 8) = 11! / (8! · 3!)

= C(11, 3)

= 165

If order matters (permutations): P(11, 8) = 11 × 10 × 9 × … × 4 = 6,652,800 — each combination in 8! = 40,320 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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See Also

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https://calculat.io/en/number/combinations/11--8

<a href="https://calculat.io/en/number/combinations/11--8">11 Choose 8: Combinations C(11, 8) - Calculatio</a>

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11 Choose 8: Combinations C(11, 8). 11 choose 8 = 165: the number of ways to choose 8 of 11 items when order doesn't matter and nothing repeats. C(11, 8) = (11 × 10 × 9) / (3 × 2 × 1).

https://calculat.io/en/number/combinations/11--8/generated.jpg

n choose 8 for other n

n choose 8	Answer
8 choose 8	1
9 choose 8	9
10 choose 8	45
11 choose 8	165
12 choose 8	495
13 choose 8	1,287
14 choose 8	3,003
15 choose 8	6,435
16 choose 8	12,870
17 choose 8	24,310
18 choose 8	43,758
19 choose 8	75,582
20 choose 8	125,970

Recalculate with different values ↑

FAQ

What is 11 choose 8?

11 choose 8 is 165

Why is 11 choose 8 the same as 11 choose 3?

Every way to choose 8 of 11 items leaves exactly 3 behind, so choosing 8 and choosing which 3 to leave out are the same count: 11 choose 8 = 11 choose 3 = 165. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(11, 8) = 6,652,800. Each of the 165 combinations can be put in order in 8! = 40,320 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.