14 Choose 6

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

What is 14 choose 6?

Answer

14 choose 6 is
3,003

Order doesn't matter, no repeats: 3,003 ways to choose 6 of 14 items.

C(14, 6) = 14! / (6! · 8!)

= (14 × 13 × 12 × 11 × 10 × 9) / (6 × 5 × 4 × 3 × 2 × 1)
= 2,162,160 / 720

= 3,003

If order matters (permutations): P(14, 6) = 14 × 13 × 12 × 11 × 10 × 9 = 2,162,160 — each combination in 6! = 720 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 6 for other n

n choose 6Answer
6 choose 61
7 choose 67
8 choose 628
9 choose 684
10 choose 6210
11 choose 6462
12 choose 6924
13 choose 61,716
14 choose 63,003
15 choose 65,005
16 choose 68,008
17 choose 612,376
18 choose 618,564
19 choose 627,132
20 choose 638,760

FAQ

What is 14 choose 6?

14 choose 6 is 3,003

Why is 14 choose 6 the same as 14 choose 8?

Every way to choose 6 of 14 items leaves exactly 8 behind, so choosing 6 and choosing which 8 to leave out are the same count: 14 choose 6 = 14 choose 8 = 3,003. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(14, 6) = 2,162,160. Each of the 3,003 combinations can be put in order in 6! = 720 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also