100 Choose 3

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

What is 100 choose 3?

Answer

100 choose 3 is
161,700

Order doesn't matter, no repeats: 161,700 ways to choose 3 of 100 items.

C(100, 3) = 100! / (3! · 97!)

= (100 × 99 × 98) / (3 × 2 × 1)
= 970,200 / 6

= 161,700

If order matters (permutations): P(100, 3) = 100 × 99 × 98 = 970,200 — each combination in 3! = 6 orders.

Row 100 of Pascal's triangle
k100 choose k
01
1100
24,950
3161,700
43,921,225
575,287,520
61,192,052,400
……
1001

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 100 choose 3?

100 choose 3 is 161,700

Why is 100 choose 3 the same as 100 choose 97?

Every way to choose 3 of 100 items leaves exactly 97 behind, so choosing 3 and choosing which 97 to leave out are the same count: 100 choose 3 = 100 choose 97 = 161,700. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(100, 3) = 970,200. Each of the 161,700 combinations can be put in order in 3! = 6 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also