17 Choose 7

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

What is 17 choose 7?

Answer

17 choose 7 is
19,448

Order doesn't matter, no repeats: 19,448 ways to choose 7 of 17 items.

C(17, 7) = 17! / (7! · 10!)

= (17 × 16 × 15 × … × 11) / (7 × 6 × 5 × … × 1)

7 factors on top and bottom

= 98,017,920 / 5,040

= 19,448

If order matters (permutations): P(17, 7) = 17 × 16 × 15 × … × 11 = 98,017,920 — each combination in 7! = 5,040 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 7 for other n

n choose 7Answer
7 choose 71
8 choose 78
9 choose 736
10 choose 7120
11 choose 7330
12 choose 7792
13 choose 71,716
14 choose 73,432
15 choose 76,435
16 choose 711,440
17 choose 719,448
18 choose 731,824
19 choose 750,388
20 choose 777,520

FAQ

What is 17 choose 7?

17 choose 7 is 19,448

Why is 17 choose 7 the same as 17 choose 10?

Every way to choose 7 of 17 items leaves exactly 10 behind, so choosing 7 and choosing which 10 to leave out are the same count: 17 choose 7 = 17 choose 10 = 19,448. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(17, 7) = 98,017,920. Each of the 19,448 combinations can be put in order in 7! = 5,040 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also