7 choose 5
Choosing 5 from 7— order doesn't matter.
Combinations (order doesn't matter)
7C5 = 21
Permutations (order matters): 7P5 = 2,520
There are 21 ways to choose 5 items from 7when order doesn't matter, using the formula C(n, k) = n! / (k! · (n − k)!).
7 choose k table
| Expression | Combinations |
|---|---|
| 7 choose 0 | 1 |
| 7 choose 1 | 7 |
| 7 choose 2 | 21 |
| 7 choose 3 | 35 |
| 7 choose 4 | 35 |
| 7 choose 5 | 21 |
| 7 choose 6 | 7 |
| 7 choose 7 | 1 |
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Need different values? The full permutations & combinations calculator computes nCr and nPr for any n and k.
Frequently asked questions
What is 7 choose 5?+
7 choose 5 equals 21. It counts the number of ways to choose 5 items from 7 when the order does not matter.
What is the formula for 7 choose 5?+
The combinations formula is C(n, k) = n! / (k! · (n − k)!). For 7 choose 5: 7! / (5! · 2!) = 21.