40 Choose 3

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

What is 40 choose 3?

Answer

40 choose 3 is
9,880

Order doesn't matter, no repeats: 9,880 ways to choose 3 of 40 items.

C(40, 3) = 40! / (3! · 37!)

= (40 × 39 × 38) / (3 × 2 × 1)
= 59,280 / 6

= 9,880

If order matters (permutations): P(40, 3) = 40 × 39 × 38 = 59,280 — each combination in 3! = 6 orders.

Row 40 of Pascal's triangle
k40 choose k
01
140
2780
39,880
491,390
5658,008
63,838,380
……
401

See Also

Recalculate with different values ↑

n choose 3 for other n

n choose 3Answer
9 choose 384
10 choose 3120
11 choose 3165
12 choose 3220
13 choose 3286
14 choose 3364
15 choose 3455
16 choose 3560
17 choose 3680
18 choose 3816
19 choose 3969
20 choose 31,140
25 choose 32,300
40 choose 39,880
100 choose 3161,700

FAQ

What is 40 choose 3?

40 choose 3 is 9,880

Why is 40 choose 3 the same as 40 choose 37?

Every way to choose 3 of 40 items leaves exactly 37 behind, so choosing 3 and choosing which 37 to leave out are the same count: 40 choose 3 = 40 choose 37 = 9,880. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(40, 3) = 59,280. Each of the 9,880 combinations can be put in order in 3! = 6 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also