14 Choose 13

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Total items (n)
Items chosen (k)

What is 14 choose 13?

Answer

14 choose 13 is
14

Order doesn't matter, no repeats: 14 ways to choose 13 of 14 items.

Choosing 13 of 14 is the same as leaving 1 out: C(14, 13) = C(14, 1).

C(14, 13) = 14! / (13! · 1!)

= C(14, 1)

= 14 / 1

= 14

If order matters (permutations): P(14, 13) = 14 × 13 × 12 × … × 2 = 87,178,291,200 — each combination in 13! = 6,227,020,800 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 13 for other n

n choose 13Answer
13 choose 131
14 choose 1314
15 choose 13105
16 choose 13560
17 choose 132,380
18 choose 138,568
19 choose 1327,132
20 choose 1377,520

FAQ

What is 14 choose 13?

14 choose 13 is 14

Why is 14 choose 13 the same as 14 choose 1?

Every way to choose 13 of 14 items leaves exactly 1 behind, so choosing 13 and choosing which one to leave out are the same count: 14 choose 13 = 14 choose 1 = 14. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(14, 13) = 87,178,291,200. Each of the 14 combinations can be put in order in 13! = 6,227,020,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also