17 Choose 8

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

What is 17 choose 8?

Answer

17 choose 8 is
24,310

Order doesn't matter, no repeats: 24,310 ways to choose 8 of 17 items.

C(17, 8) = 17! / (8! · 9!)

= (17 × 16 × 15 × … × 10) / (8 × 7 × 6 × … × 1)

8 factors on top and bottom

= 980,179,200 / 40,320

= 24,310

If order matters (permutations): P(17, 8) = 17 × 16 × 15 × … × 10 = 980,179,200 — each combination in 8! = 40,320 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 8 for other n

n choose 8Answer
8 choose 81
9 choose 89
10 choose 845
11 choose 8165
12 choose 8495
13 choose 81,287
14 choose 83,003
15 choose 86,435
16 choose 812,870
17 choose 824,310
18 choose 843,758
19 choose 875,582
20 choose 8125,970

FAQ

What is 17 choose 8?

17 choose 8 is 24,310

Why is 17 choose 8 the same as 17 choose 9?

Every way to choose 8 of 17 items leaves exactly 9 behind, so choosing 8 and choosing which 9 to leave out are the same count: 17 choose 8 = 17 choose 9 = 24,310. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(17, 8) = 980,179,200. Each of the 24,310 combinations can be put in order in 8! = 40,320 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also