17 Choose 10

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

What is 17 choose 10?

Answer

17 choose 10 is
19,448

Order doesn't matter, no repeats: 19,448 ways to choose 10 of 17 items.

Choosing 10 of 17 is the same as leaving 7 out: C(17, 10) = C(17, 7).

C(17, 10) = 17! / (10! · 7!)

= C(17, 7)

= (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, 10) = 17 × 16 × 15 × … × 8 = 70,572,902,400 — each combination in 10! = 3,628,800 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 10 for other n

n choose 10Answer
2 choose 100
10 choose 101
11 choose 1011
12 choose 1066
13 choose 10286
14 choose 101,001
15 choose 103,003
16 choose 108,008
17 choose 1019,448
18 choose 1043,758
19 choose 1092,378
20 choose 10184,756
100 choose 1017,310,309,456,440

FAQ

What is 17 choose 10?

17 choose 10 is 19,448

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

Every way to choose 10 of 17 items leaves exactly 7 behind, so choosing 10 and choosing which 7 to leave out are the same count: 17 choose 10 = 17 choose 7 = 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, 10) = 70,572,902,400. Each of the 19,448 combinations can be put in order in 10! = 3,628,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also