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10 Choose 10

Combination Calculator

What is 10 choose 10?

Answer

10 choose 10 is

1

Order doesn't matter, no repeats: 1 way to choose 10 of 10 items.

There is exactly one way: take all.

C(10, 10) = 10! / (10! · 0!)

= 1

0! = 1 (an empty product), so 10! cancels out completely.

If order matters (permutations): P(10, 10) = 10 × 9 × 8 × … × 1 = 3,628,800 — each combination in 10! = 3,628,800 orders.

Row 10 of Pascal's triangle
k	10 choose k
0	1
1	10
2	45
3	120
4	210
5	252
6	210
7	120
8	45
9	10
10	1

Row sum: 2¹⁰ = 1,024 — all subsets of 10 items.

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See Also

Random Number Generator - Pick a random whole number between two bounds
Percent to Probability Converter - Convert Percents to "1 in X" Probability Chance
Factors of a Number - List all Factors and Factor Pairs of a Number

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https://calculat.io/en/number/combinations/10--10

<a href="https://calculat.io/en/number/combinations/10--10">10 Choose 10: Combinations C(10, 10) - Calculatio</a>

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10 Choose 10: Combinations C(10, 10). 10 choose 10 = 1: the number of ways to choose 10 of 10 items when order doesn't matter and nothing repeats.

https://calculat.io/en/number/combinations/10--10/generated.jpg

n choose 10 for other n

n choose 10	Answer
2 choose 10	0
10 choose 10	1
11 choose 10	11
12 choose 10	66
13 choose 10	286
14 choose 10	1,001
15 choose 10	3,003
16 choose 10	8,008
17 choose 10	19,448
18 choose 10	43,758
19 choose 10	92,378
20 choose 10	184,756
100 choose 10	17,310,309,456,440

Recalculate with different values ↑

FAQ

What is 10 choose 10?

10 choose 10 is 1

Why is 10 choose 10 the same as 10 choose 0?

Every way to choose 10 of 10 items leaves exactly 0 behind, so choosing 10 and choosing which 0 to leave out are the same count: 10 choose 10 = 10 choose 0 = 1. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(10, 10) = 3,628,800. The only combination — all 10 items — can be put in order in 10! = 3,628,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.