17 Choose 15

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

What is 17 choose 15?

Answer

17 choose 15 is
136

Order doesn't matter, no repeats: 136 ways to choose 15 of 17 items.

Choosing 15 of 17 is the same as leaving 2 out: C(17, 15) = C(17, 2).

C(17, 15) = 17! / (15! · 2!)

= C(17, 2)

= (17 × 16) / (2 × 1)
= 272 / 2

= 136

If order matters (permutations): P(17, 15) = 17 × 16 × 15 × … × 3 = 177,843,714,048,000 — each combination in 15! = 1,307,674,368,000 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 15 for other n

n choose 15Answer
15 choose 151
16 choose 1516
17 choose 15136
18 choose 15816
19 choose 153,876
20 choose 1515,504

FAQ

What is 17 choose 15?

17 choose 15 is 136

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

Every way to choose 15 of 17 items leaves exactly 2 behind, so choosing 15 and choosing which 2 to leave out are the same count: 17 choose 15 = 17 choose 2 = 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, 15) = 177,843,714,048,000. Each of the 136 combinations can be put in order in 15! = 1,307,674,368,000 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also