14 Choose 14

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Total items (n)
Items chosen (k)

What is 14 choose 14?

Answer

14 choose 14 is
1

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

There is exactly one way: take all.

C(14, 14) = 14! / (14! · 0!)

= 1

0! = 1 (an empty product), so 14! cancels out completely.

If order matters (permutations): P(14, 14) = 14 × 13 × 12 × … × 1 = 87,178,291,200 — each combination in 14! = 87,178,291,200 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 14 for other n

n choose 14Answer
14 choose 141
15 choose 1415
16 choose 14120
17 choose 14680
18 choose 143,060
19 choose 1411,628
20 choose 1438,760

FAQ

What is 14 choose 14?

14 choose 14 is 1

Why is 14 choose 14 the same as 14 choose 0?

Every way to choose 14 of 14 items leaves exactly 0 behind, so choosing 14 and choosing which 0 to leave out are the same count: 14 choose 14 = 14 choose 0 = 1. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(14, 14) = 87,178,291,200. The only combination — all 14 items — can be put in order in 14! = 87,178,291,200 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also