25 Choose 3

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

What is 25 choose 3?

Answer

25 choose 3 is
2,300

Order doesn't matter, no repeats: 2,300 ways to choose 3 of 25 items.

C(25, 3) = 25! / (3! · 22!)

= (25 × 24 × 23) / (3 × 2 × 1)
= 13,800 / 6

= 2,300

If order matters (permutations): P(25, 3) = 25 × 24 × 23 = 13,800 — each combination in 3! = 6 orders.

Row 25 of Pascal's triangle
k25 choose k
01
125
2300
32,300
412,650
553,130
6177,100
……
251

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 25 choose 3?

25 choose 3 is 2,300

Why is 25 choose 3 the same as 25 choose 22?

Every way to choose 3 of 25 items leaves exactly 22 behind, so choosing 3 and choosing which 22 to leave out are the same count: 25 choose 3 = 25 choose 22 = 2,300. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(25, 3) = 13,800. Each of the 2,300 combinations can be put in order in 3! = 6 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also