Combinations Calculator
C(n,r) — order does not matter
Combinations count ways to choose items where order does not matter. Permutations count ways where order does matter. Both use factorials and appear in probability, statistics, and combinatorics.
- 1Permutations (order matters): P(n,r) = n! / (n−r)!
- 2Combinations (order irrelevant): C(n,r) = n! / (r!(n−r)!)
- 3Rule of thumb: if you can swap two items and get a different result, use permutations
Choose 3 from 10 (order matters)=720P(10,3) = 10×9×8 = 720
Choose 3 from 10 (order irrelevant)=120C(10,3) = 720/6 = 120
Lotto: 6 from 49=13,983,816C(49,6)
| Scenario | Type | Formula |
|---|---|---|
| Picking a PIN code | Permutation | P(10,4) = 5,040 |
| Lottery numbers | Combination | C(49,6) = 13,983,816 |
| Race podium (1st/2nd/3rd) | Permutation | P(n,3) |
| Committee selection | Combination | C(n,3) |
| Card hand (5 cards) | Combination | C(52,5) = 2,598,960 |
⭐
Fun Fact
There are C(52,5) = 2,598,960 possible 5-card poker hands from a standard deck, but only 4 are Royal Flushes — odds of 1 in 649,740.
References
🔒
୧୦୦% ମାଗଣା
ପଞ୍ଜୀକରଣ ଆବଶ୍ୟକ ନାହିଁ
✓
ସଠିକ
ଯାଞ୍ଚ ହୋଇଥିବା ସୂତ୍ର
⚡
ତତ୍କ୍ଷଣ
ତତ୍କ୍ଷଣ ଫଳ
📱
ମୋବାଇଲ୍ ଅନୁକୂଳ
ସମସ୍ତ ଡିଭାଇସ୍