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12 Choose 8

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What is 12 choose 8?

Answer

12 choose 8 is

495

Order doesn't matter, no repeats: 495 ways to choose 8 of 12 items.

Choosing 8 of 12 is the same as leaving 4 out: C(12, 8) = C(12, 4).

C(12, 8) = 12! / (8! · 4!)

= C(12, 4)

= 495

If order matters (permutations): P(12, 8) = 12 × 11 × 10 × … × 5 = 19,958,400 — each combination in 8! = 40,320 orders.

Row 12 of Pascal's triangle
k	12 choose k
0	1
1	12
2	66
3	220
4	495
5	792
6	924
7	792
8	495
9	220
10	66
11	12
12	1

Row sum: 2¹² = 4,096 — all subsets of 12 items.

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https://calculat.io/en/number/combinations/12--8

<a href="https://calculat.io/en/number/combinations/12--8">12 Choose 8: Combinations C(12, 8) - Calculatio</a>

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12 Choose 8: Combinations C(12, 8). 12 choose 8 = 495: the number of ways to choose 8 of 12 items when order doesn't matter and nothing repeats. C(12, 8) = (12 × 11 × 10 × 9) / (4 × 3 × 2 × 1).

https://calculat.io/en/number/combinations/12--8/generated.jpg

n choose 8 for other n

n choose 8	Answer
8 choose 8	1
9 choose 8	9
10 choose 8	45
11 choose 8	165
12 choose 8	495
13 choose 8	1,287
14 choose 8	3,003
15 choose 8	6,435
16 choose 8	12,870
17 choose 8	24,310
18 choose 8	43,758
19 choose 8	75,582
20 choose 8	125,970

Recalculate with different values ↑

FAQ

What is 12 choose 8?

12 choose 8 is 495

Why is 12 choose 8 the same as 12 choose 4?

Every way to choose 8 of 12 items leaves exactly 4 behind, so choosing 8 and choosing which 4 to leave out are the same count: 12 choose 8 = 12 choose 4 = 495. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(12, 8) = 19,958,400. Each of the 495 combinations can be put in order in 8! = 40,320 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.