17 Choose 9

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

What is 17 choose 9?

Answer

17 choose 9 is
24,310

Order doesn't matter, no repeats: 24,310 ways to choose 9 of 17 items.

Choosing 9 of 17 is the same as leaving 8 out: C(17, 9) = C(17, 8).

C(17, 9) = 17! / (9! · 8!)

= C(17, 8)

= (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, 9) = 17 × 16 × 15 × … × 9 = 8,821,612,800 — each combination in 9! = 362,880 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 9 for other n

n choose 9Answer
9 choose 91
10 choose 910
11 choose 955
12 choose 9220
13 choose 9715
14 choose 92,002
15 choose 95,005
16 choose 911,440
17 choose 924,310
18 choose 948,620
19 choose 992,378
20 choose 9167,960

FAQ

What is 17 choose 9?

17 choose 9 is 24,310

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

Every way to choose 9 of 17 items leaves exactly 8 behind, so choosing 9 and choosing which 8 to leave out are the same count: 17 choose 9 = 17 choose 8 = 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, 9) = 8,821,612,800. Each of the 24,310 combinations can be put in order in 9! = 362,880 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also