17 Choose 4

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

What is 17 choose 4?

Answer

17 choose 4 is
2,380

Order doesn't matter, no repeats: 2,380 ways to choose 4 of 17 items.

C(17, 4) = 17! / (4! · 13!)

= (17 × 16 × 15 × 14) / (4 × 3 × 2 × 1)
= 57,120 / 24

= 2,380

If order matters (permutations): P(17, 4) = 17 × 16 × 15 × 14 = 57,120 — each combination in 4! = 24 orders.

Row 17 of Pascal's triangle
k17 choose k
01
117
2136
3680
42,380
56,188
612,376
719,448
824,310
924,310
1019,448
1112,376
126,188
132,380
14680
15136
1617
171

Row sum: 217 = 131,072 — all subsets of 17 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 17 choose 4?

17 choose 4 is 2,380

Why is 17 choose 4 the same as 17 choose 13?

Every way to choose 4 of 17 items leaves exactly 13 behind, so choosing 4 and choosing which 13 to leave out are the same count: 17 choose 4 = 17 choose 13 = 2,380. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(17, 4) = 57,120. Each of the 2,380 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also