13 Choose 7
Combination Calculator
What is 13 choose 7?
Answer
13 choose 7 is
1,716
Order doesn't matter, no repeats: 1,716 ways to choose 7 of 13 items.
Choosing 7 of 13 is the same as leaving 6 out: C(13, 7) = C(13, 6).
C(13, 7) = 13! / (7! · 6!)
= C(13, 6)
= (13 × 12 × 11 × 10 × 9 × 8) / (6 × 5 × 4 × 3 × 2 × 1)
= 1,235,520 / 720
= 1,716
If order matters (permutations): P(13, 7) = 13 × 12 × 11 × … × 7 = 8,648,640 — each combination in 7! = 5,040 orders.
Row sum: 213 = 8,192 — all subsets of 13 items.
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See Also
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