14 Choose 11

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Total items (n)
Items chosen (k)

What is 14 choose 11?

Answer

14 choose 11 is
364

Order doesn't matter, no repeats: 364 ways to choose 11 of 14 items.

Choosing 11 of 14 is the same as leaving 3 out: C(14, 11) = C(14, 3).

C(14, 11) = 14! / (11! · 3!)

= C(14, 3)

= (14 × 13 × 12) / (3 × 2 × 1)
= 2,184 / 6

= 364

If order matters (permutations): P(14, 11) = 14 × 13 × 12 × … × 4 = 14,529,715,200 — each combination in 11! = 39,916,800 orders.

Row 14 of Pascal's triangle
k14 choose k
01
114
291
3364
41,001
52,002
63,003
73,432
83,003
92,002
101,001
11364
1291
1314
141

Row sum: 214 = 16,384 — all subsets of 14 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 14 choose 11?

14 choose 11 is 364

Why is 14 choose 11 the same as 14 choose 3?

Every way to choose 11 of 14 items leaves exactly 3 behind, so choosing 11 and choosing which 3 to leave out are the same count: 14 choose 11 = 14 choose 3 = 364. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(14, 11) = 14,529,715,200. Each of the 364 combinations can be put in order in 11! = 39,916,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also