14 Choose 5

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

What is 14 choose 5?

Answer

14 choose 5 is
2,002

Order doesn't matter, no repeats: 2,002 ways to choose 5 of 14 items.

C(14, 5) = 14! / (5! · 9!)

= (14 × 13 × 12 × 11 × 10) / (5 × 4 × 3 × 2 × 1)
= 240,240 / 120

= 2,002

If order matters (permutations): P(14, 5) = 14 × 13 × 12 × 11 × 10 = 240,240 — each combination in 5! = 120 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 5 for other n

n choose 5Answer
6 choose 56
7 choose 521
8 choose 556
9 choose 5126
10 choose 5252
11 choose 5462
12 choose 5792
13 choose 51,287
14 choose 52,002
15 choose 53,003
16 choose 54,368
17 choose 56,188
18 choose 58,568
19 choose 511,628
20 choose 515,504

FAQ

What is 14 choose 5?

14 choose 5 is 2,002

Why is 14 choose 5 the same as 14 choose 9?

Every way to choose 5 of 14 items leaves exactly 9 behind, so choosing 5 and choosing which 9 to leave out are the same count: 14 choose 5 = 14 choose 9 = 2,002. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(14, 5) = 240,240. Each of the 2,002 combinations can be put in order in 5! = 120 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also