16 Choose 14

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

What is 16 choose 14?

Answer

16 choose 14 is
120

Order doesn't matter, no repeats: 120 ways to choose 14 of 16 items.

Choosing 14 of 16 is the same as leaving 2 out: C(16, 14) = C(16, 2).

C(16, 14) = 16! / (14! · 2!)

= C(16, 2)

= (16 × 15) / (2 × 1)
= 240 / 2

= 120

If order matters (permutations): P(16, 14) = 16 × 15 × 14 × … × 3 = 10,461,394,944,000 — each combination in 14! = 87,178,291,200 orders.

Row 16 of Pascal's triangle
k16 choose k
01
116
2120
3560
41,820
54,368
68,008
711,440
812,870
911,440
108,008
114,368
121,820
13560
14120
1516
161

Row sum: 216 = 65,536 — all subsets of 16 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 16 choose 14?

16 choose 14 is 120

Why is 16 choose 14 the same as 16 choose 2?

Every way to choose 14 of 16 items leaves exactly 2 behind, so choosing 14 and choosing which 2 to leave out are the same count: 16 choose 14 = 16 choose 2 = 120. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(16, 14) = 10,461,394,944,000. Each of the 120 combinations can be put in order in 14! = 87,178,291,200 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also