7 Choose 3

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

What is 7 choose 3?

Answer

7 choose 3 is
35

Order doesn't matter, no repeats: 35 ways to choose 3 of 7 items.

C(7, 3) = 7! / (3! · 4!)

= (7 × 6 × 5) / (3 × 2 × 1)
= 210 / 6

= 35

If order matters (permutations): P(7, 3) = 7 × 6 × 5 = 210 — each combination in 3! = 6 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 3 for other n

n choose 3Answer
1 choose 30
2 choose 30
3 choose 31
4 choose 34
5 choose 310
6 choose 320
7 choose 335
8 choose 356
9 choose 384
10 choose 3120
11 choose 3165
12 choose 3220
13 choose 3286
14 choose 3364
15 choose 3455

FAQ

What is 7 choose 3?

7 choose 3 is 35

Why is 7 choose 3 the same as 7 choose 4?

Every way to choose 3 of 7 items leaves exactly 4 behind, so choosing 3 and choosing which 4 to leave out are the same count: 7 choose 3 = 7 choose 4 = 35. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(7, 3) = 210. Each of the 35 combinations can be put in order in 3! = 6 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also