10 choose 10
Choosing 10 from 10— order doesn't matter.
Combinations (order doesn't matter)
10C10 = 1
Permutations (order matters): 10P10 = 3,628,800
There are 1 ways to choose 10 items from 10when order doesn't matter, using the formula C(n, k) = n! / (k! · (n − k)!).
10 choose k table
| Expression | Combinations |
|---|---|
| 10 choose 0 | 1 |
| 10 choose 1 | 10 |
| 10 choose 2 | 45 |
| 10 choose 3 | 120 |
| 10 choose 4 | 210 |
| 10 choose 5 | 252 |
| 10 choose 6 | 210 |
| 10 choose 7 | 120 |
| 10 choose 8 | 45 |
| 10 choose 9 | 10 |
| 10 choose 10 | 1 |
Try your own numbers
Need different values? The full permutations & combinations calculator computes nCr and nPr for any n and k.
Frequently asked questions
What is 10 choose 10?+
10 choose 10 equals 1. It counts the number of ways to choose 10 items from 10 when the order does not matter.
What is the formula for 10 choose 10?+
The combinations formula is C(n, k) = n! / (k! · (n − k)!). For 10 choose 10: 10! / (10! · 0!) = 1.