14 Choose 10

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

What is 14 choose 10?

Answer

14 choose 10 is
1,001

Order doesn't matter, no repeats: 1,001 ways to choose 10 of 14 items.

Choosing 10 of 14 is the same as leaving 4 out: C(14, 10) = C(14, 4).

C(14, 10) = 14! / (10! · 4!)

= C(14, 4)

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

= 1,001

If order matters (permutations): P(14, 10) = 14 × 13 × 12 × … × 5 = 3,632,428,800 — each combination in 10! = 3,628,800 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 10 for other n

n choose 10Answer
2 choose 100
10 choose 101
11 choose 1011
12 choose 1066
13 choose 10286
14 choose 101,001
15 choose 103,003
16 choose 108,008
17 choose 1019,448
18 choose 1043,758
19 choose 1092,378
20 choose 10184,756
100 choose 1017,310,309,456,440

FAQ

What is 14 choose 10?

14 choose 10 is 1,001

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

Every way to choose 10 of 14 items leaves exactly 4 behind, so choosing 10 and choosing which 4 to leave out are the same count: 14 choose 10 = 14 choose 4 = 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, 10) = 3,632,428,800. Each of the 1,001 combinations can be put in order in 10! = 3,628,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also