20 Choose 11

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

What is 20 choose 11?

Answer

20 choose 11 is
167,960

Order doesn't matter, no repeats: 167,960 ways to choose 11 of 20 items.

Choosing 11 of 20 is the same as leaving 9 out: C(20, 11) = C(20, 9).

C(20, 11) = 20! / (11! · 9!)

= C(20, 9)

= (20 × 19 × 18 × … × 12) / (9 × 8 × 7 × … × 1)

9 factors on top and bottom

= 60,949,324,800 / 362,880

= 167,960

If order matters (permutations): P(20, 11) = 20 × 19 × 18 × … × 10 = 6,704,425,728,000 — each combination in 11! = 39,916,800 orders.

Row 20 of Pascal's triangle
k20 choose k
01
120
2190
31,140
44,845
515,504
638,760
777,520
8125,970
9167,960
10184,756
11167,960
12125,970
1377,520
1438,760
1515,504
164,845
171,140
18190
1920
201

Row sum: 220 = 1,048,576 — all subsets of 20 items.

See Also

Recalculate with different values ↑

n choose 11 for other n

n choose 11Answer
11 choose 111
12 choose 1112
13 choose 1178
14 choose 11364
15 choose 111,365
16 choose 114,368
17 choose 1112,376
18 choose 1131,824
19 choose 1175,582
20 choose 11167,960

FAQ

What is 20 choose 11?

20 choose 11 is 167,960

Why is 20 choose 11 the same as 20 choose 9?

Every way to choose 11 of 20 items leaves exactly 9 behind, so choosing 11 and choosing which 9 to leave out are the same count: 20 choose 11 = 20 choose 9 = 167,960. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(20, 11) = 6,704,425,728,000. Each of the 167,960 combinations can be put in order in 11! = 39,916,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also