7 Choose 7

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

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
k7 choose k
01
17
221
335
435
521
67
71

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

See Also

Recalculate with different values ↑

n choose 7 for other n

n choose 7Answer
7 choose 71
8 choose 78
9 choose 736
10 choose 7120
11 choose 7330
12 choose 7792
13 choose 71,716
14 choose 73,432
15 choose 76,435
16 choose 711,440
17 choose 719,448
18 choose 731,824
19 choose 750,388
20 choose 777,520

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)!.

See Also