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7 Choose 7

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What is 7 choose 7?

Answer

7 choose 7 is

1

Order doesn't matter, no repeats: 1 way to choose 7 of 7 items.

There is exactly one way: take all.

C(7, 7) = 7! / (7! · 0!)

= 1

0! = 1 (an empty product), so 7! cancels out completely.

If order matters (permutations): P(7, 7) = 7 × 6 × 5 × … × 1 = 5,040 — each combination in 7! = 5,040 orders.

Row 7 of Pascal's triangle
k	7 choose k
0	1
1	7
2	21
3	35
4	35
5	21
6	7
7	1

Row sum: 2⁷ = 128 — all subsets of 7 items.

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See Also

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https://calculat.io/en/number/combinations/7--7

<a href="https://calculat.io/en/number/combinations/7--7">7 Choose 7: Combinations C(7, 7) - Calculatio</a>

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7 Choose 7: Combinations C(7, 7). 7 choose 7 = 1: the number of ways to choose 7 of 7 items when order doesn't matter and nothing repeats.

https://calculat.io/en/number/combinations/7--7/generated.jpg

n choose 7 for other n

n choose 7	Answer
7 choose 7	1
8 choose 7	8
9 choose 7	36
10 choose 7	120
11 choose 7	330
12 choose 7	792
13 choose 7	1,716
14 choose 7	3,432
15 choose 7	6,435
16 choose 7	11,440
17 choose 7	19,448
18 choose 7	31,824
19 choose 7	50,388
20 choose 7	77,520

Recalculate with different values ↑

FAQ

What is 7 choose 7?

7 choose 7 is 1

Why is 7 choose 7 the same as 7 choose 0?

Every way to choose 7 of 7 items leaves exactly 0 behind, so choosing 7 and choosing which 0 to leave out are the same count: 7 choose 7 = 7 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(7, 7) = 5,040. The only combination — all 7 items — can be put in order in 7! = 5,040 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.