14 Choose 3

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

What is 14 choose 3?

Answer

14 choose 3 is
364

Order doesn't matter, no repeats: 364 ways to choose 3 of 14 items.

C(14, 3) = 14! / (3! · 11!)

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

= 364

If order matters (permutations): P(14, 3) = 14 × 13 × 12 = 2,184 — each combination in 3! = 6 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 3 for other n

n choose 3Answer
7 choose 335
8 choose 356
9 choose 384
10 choose 3120
11 choose 3165
12 choose 3220
13 choose 3286
14 choose 3364
15 choose 3455
16 choose 3560
17 choose 3680
18 choose 3816
19 choose 3969
20 choose 31,140
25 choose 32,300

FAQ

What is 14 choose 3?

14 choose 3 is 364

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

Every way to choose 3 of 14 items leaves exactly 11 behind, so choosing 3 and choosing which 11 to leave out are the same count: 14 choose 3 = 14 choose 11 = 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, 3) = 2,184. Each of the 364 combinations can be put in order in 3! = 6 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also