14 Choose 4

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

What is 14 choose 4?

Answer

14 choose 4 is
1,001

Order doesn't matter, no repeats: 1,001 ways to choose 4 of 14 items.

C(14, 4) = 14! / (4! · 10!)

= (14 × 13 × 12 × 11) / (4 × 3 × 2 × 1)
= 24,024 / 24

= 1,001

If order matters (permutations): P(14, 4) = 14 × 13 × 12 × 11 = 24,024 — each combination in 4! = 24 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 4 for other n

n choose 4Answer
7 choose 435
8 choose 470
9 choose 4126
10 choose 4210
11 choose 4330
12 choose 4495
13 choose 4715
14 choose 41,001
15 choose 41,365
16 choose 41,820
17 choose 42,380
18 choose 43,060
19 choose 43,876
20 choose 44,845
24 choose 410,626

FAQ

What is 14 choose 4?

14 choose 4 is 1,001

Why is 14 choose 4 the same as 14 choose 10?

Every way to choose 4 of 14 items leaves exactly 10 behind, so choosing 4 and choosing which 10 to leave out are the same count: 14 choose 4 = 14 choose 10 = 1,001. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(14, 4) = 24,024. Each of the 1,001 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also