Carla selects 5 fruit-flavored candies from a bowl containing 6 apple, 5 banana and 4 cherry candies.
How many possible combinations of candies can Carla select?
The answer is 20, but how do I get it?
+9519 Consider the cases where you pick 0, 1, 2, 3, 4 cherry candies respectively. You can calculate how many candies you can pick after picking some amount of cherry candies, and suppose you can pick k more candies after picking some cherry candies, these are the only cases:
| Apple candies | Banana candies |
|---|---|
| 0 | k |
| 1 | k - 1 |
| ... | ... |
| k | 0 |
So if you are to pick k more candies from apple candies and banana candies, you would have k + 1 cases (just set k to some small number and count the number of rows in the table above).
Now you should be able to manually count the cases.
