14 Choose 9

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

What is 14 choose 9?

Answer

14 choose 9 is
2,002

Order doesn't matter, no repeats: 2,002 ways to choose 9 of 14 items.

Choosing 9 of 14 is the same as leaving 5 out: C(14, 9) = C(14, 5).

C(14, 9) = 14! / (9! · 5!)

= C(14, 5)

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

= 2,002

If order matters (permutations): P(14, 9) = 14 × 13 × 12 × … × 6 = 726,485,760 — each combination in 9! = 362,880 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 9 for other n

n choose 9Answer
9 choose 91
10 choose 910
11 choose 955
12 choose 9220
13 choose 9715
14 choose 92,002
15 choose 95,005
16 choose 911,440
17 choose 924,310
18 choose 948,620
19 choose 992,378
20 choose 9167,960

FAQ

What is 14 choose 9?

14 choose 9 is 2,002

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

Every way to choose 9 of 14 items leaves exactly 5 behind, so choosing 9 and choosing which 5 to leave out are the same count: 14 choose 9 = 14 choose 5 = 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, 9) = 726,485,760. Each of the 2,002 combinations can be put in order in 9! = 362,880 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also