16 Choose 4

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

What is 16 choose 4?

Answer

16 choose 4 is
1,820

Order doesn't matter, no repeats: 1,820 ways to choose 4 of 16 items.

C(16, 4) = 16! / (4! · 12!)

= (16 × 15 × 14 × 13) / (4 × 3 × 2 × 1)
= 43,680 / 24

= 1,820

If order matters (permutations): P(16, 4) = 16 × 15 × 14 × 13 = 43,680 — each combination in 4! = 24 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 4 for other n

n choose 4Answer
7 choose 435
8 choose 470
9 choose 4126
10 choose 4210
11 choose 4330
12 choose 4495
13 choose 4715
14 choose 41,001
15 choose 41,365
16 choose 41,820
17 choose 42,380
18 choose 43,060
19 choose 43,876
20 choose 44,845
24 choose 410,626

FAQ

What is 16 choose 4?

16 choose 4 is 1,820

Why is 16 choose 4 the same as 16 choose 12?

Every way to choose 4 of 16 items leaves exactly 12 behind, so choosing 4 and choosing which 12 to leave out are the same count: 16 choose 4 = 16 choose 12 = 1,820. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(16, 4) = 43,680. Each of the 1,820 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also