14 Choose 7

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

What is 14 choose 7?

Answer

14 choose 7 is
3,432

Order doesn't matter, no repeats: 3,432 ways to choose 7 of 14 items.

C(14, 7) = 14! / (7! · 7!)

= (14 × 13 × 12 × … × 8) / (7 × 6 × 5 × … × 1)

7 factors on top and bottom

= 17,297,280 / 5,040

= 3,432

If order matters (permutations): P(14, 7) = 14 × 13 × 12 × … × 8 = 17,297,280 — each combination in 7! = 5,040 orders.

Row 14 of Pascal's triangle
k14 choose k
01
114
291
3364
41,001
52,002
63,003
73,432
83,003
92,002
101,001
11364
1291
1314
141

Row sum: 214 = 16,384 — all subsets of 14 items.

See Also

Recalculate with different values ↑

n choose 7 for other n

n choose 7Answer
7 choose 71
8 choose 78
9 choose 736
10 choose 7120
11 choose 7330
12 choose 7792
13 choose 71,716
14 choose 73,432
15 choose 76,435
16 choose 711,440
17 choose 719,448
18 choose 731,824
19 choose 750,388
20 choose 777,520

FAQ

What is 14 choose 7?

14 choose 7 is 3,432

Why is 14 choose 7 the largest number in row 14?

In row 14 of Pascal's triangle the numbers grow towards the middle and shrink after it, because n choose k = n choose (n − k). With an even n the middle is k = 7, so 14 choose 7 = 3,432 is the largest: 14 choose 6 is only 3,003.

How many ways are there if order matters?

P(14, 7) = 17,297,280. Each of the 3,432 combinations can be put in order in 7! = 5,040 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also