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11 Choose 7

Combination Calculator

What is 11 choose 7?

Answer

11 choose 7 is

330

Order doesn't matter, no repeats: 330 ways to choose 7 of 11 items.

Choosing 7 of 11 is the same as leaving 4 out: C(11, 7) = C(11, 4).

C(11, 7) = 11! / (7! · 4!)

= C(11, 4)

= 330

If order matters (permutations): P(11, 7) = 11 × 10 × 9 × … × 5 = 1,663,200 — each combination in 7! = 5,040 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--7

<a href="https://calculat.io/en/number/combinations/11--7">11 Choose 7: Combinations C(11, 7) - Calculatio</a>

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11 Choose 7: Combinations C(11, 7). 11 choose 7 = 330: the number of ways to choose 7 of 11 items when order doesn't matter and nothing repeats. C(11, 7) = (11 × 10 × 9 × 8) / (4 × 3 × 2 × 1).

https://calculat.io/en/number/combinations/11--7/generated.jpg

n choose 7 for other n

n choose 7	Answer
7 choose 7	1
8 choose 7	8
9 choose 7	36
10 choose 7	120
11 choose 7	330
12 choose 7	792
13 choose 7	1,716
14 choose 7	3,432
15 choose 7	6,435
16 choose 7	11,440
17 choose 7	19,448
18 choose 7	31,824
19 choose 7	50,388
20 choose 7	77,520

Recalculate with different values ↑

FAQ

What is 11 choose 7?

11 choose 7 is 330

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

Every way to choose 7 of 11 items leaves exactly 4 behind, so choosing 7 and choosing which 4 to leave out are the same count: 11 choose 7 = 11 choose 4 = 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, 7) = 1,663,200. Each of the 330 combinations can be put in order in 7! = 5,040 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.