Feedback form

5 Choose 4

Combination Calculator

What is 5 choose 4?

Answer

5 choose 4 is

5

Order doesn't matter, no repeats: 5 ways to choose 4 of 5 items.

Choosing 4 of 5 is the same as leaving 1 out: C(5, 4) = C(5, 1).

C(5, 4) = 5! / (4! · 1!)

= C(5, 1)

= 5

If order matters (permutations): P(5, 4) = 5 × 4 × 3 × 2 = 120 — each combination in 4! = 24 orders.

Row 5 of Pascal's triangle
k	5 choose k
0	1
1	5
2	10
3	10
4	5
5	1

Row sum: 2⁵ = 32 — all subsets of 5 items.

Found an error in the calculation or the information?

See Also

Random Number Generator - Pick a random whole number between two bounds
Percent to Probability Converter - Convert Percents to "1 in X" Probability Chance
Factors of a Number - List all Factors and Factor Pairs of a Number

Share This Calculation

Print

https://calculat.io/en/number/combinations/5--4

<a href="https://calculat.io/en/number/combinations/5--4">5 Choose 4: Combinations C(5, 4) - Calculatio</a>

Facebook

Twitter

Telegram

WhatsApp

Viber

Email

5 Choose 4: Combinations C(5, 4). 5 choose 4 = 5: the number of ways to choose 4 of 5 items when order doesn't matter and nothing repeats. C(5, 4) = 5 / 1.

https://calculat.io/en/number/combinations/5--4/generated.jpg

n choose 4 for other n

n choose 4	Answer
1 choose 4	0
2 choose 4	0
3 choose 4	0
4 choose 4	1
5 choose 4	5
6 choose 4	15
7 choose 4	35
8 choose 4	70
9 choose 4	126
10 choose 4	210
11 choose 4	330
12 choose 4	495
13 choose 4	715
14 choose 4	1,001
15 choose 4	1,365

Recalculate with different values ↑

FAQ

What is 5 choose 4?

5 choose 4 is 5

Why is 5 choose 4 the same as 5 choose 1?

Every way to choose 4 of 5 items leaves exactly 1 behind, so choosing 4 and choosing which one to leave out are the same count: 5 choose 4 = 5 choose 1 = 5. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(5, 4) = 120. Each of the 5 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.