17 Choose 2

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

What is 17 choose 2?

Answer

17 choose 2 is
136

Order doesn't matter, no repeats: 136 ways to choose 2 of 17 items.

C(17, 2) = 17! / (2! · 15!)

= (17 × 16) / (2 × 1)
= 272 / 2

= 136

If order matters (permutations): P(17, 2) = 17 × 16 = 272 — each combination in 2! = 2 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 2 for other n

n choose 2Answer
6 choose 215
7 choose 221
8 choose 228
9 choose 236
10 choose 245
11 choose 255
12 choose 266
13 choose 278
14 choose 291
15 choose 2105
16 choose 2120
17 choose 2136
18 choose 2153
19 choose 2171
20 choose 2190

FAQ

What is 17 choose 2?

17 choose 2 is 136

Why is 17 choose 2 the same as 17 choose 15?

Every way to choose 2 of 17 items leaves exactly 15 behind, so choosing 2 and choosing which 15 to leave out are the same count: 17 choose 2 = 17 choose 15 = 136. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(17, 2) = 272. Each of the 136 combinations can be put in order in 2! = 2 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also