7 Choose 1

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

What is 7 choose 1?

Answer

7 choose 1 is
7

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

C(7, 1) = 7! / (1! · 6!)

= 7 / 1

= 7

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 1 for other n

n choose 1Answer
1 choose 11
2 choose 12
3 choose 13
4 choose 14
5 choose 15
6 choose 16
7 choose 17
8 choose 18
9 choose 19
10 choose 110
11 choose 111
12 choose 112
13 choose 113
14 choose 114
15 choose 115

FAQ

What is 7 choose 1?

7 choose 1 is 7

Why is 7 choose 1 the same as 7 choose 6?

Every way to choose 1 of 7 items leaves exactly 6 behind, so choosing 1 and choosing which 6 to leave out are the same count: 7 choose 1 = 7 choose 6 = 7. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

The same 7: with 1 chosen item there is only one order, so P(7, 1) = 7 choose 1 = 7. Order starts to matter from 2 items on: n × (n − 1) arrangements.

See Also