Final answer:
The formula for combinations with repetition in combinatorics is C(n+r-1,r), where n is the total number of items and r represents how many items to choose. For example, selecting 3 ice cream scoops out of 5 flavors will yield 35 combinations. If choosing 10 marbles form a bag of 100 marbles with 3 different colors, there are 66 combinations.
Step-by-step explanation:
In the field of combinatorics, the formula for combinations with repetition allows counting different combinations where repetition of elements is allowed. This is represented by the formula C(n+r-1,r), where n is the total number of items and r is the number of items to choose.
For example, if you wanted to select 3 scoops from 5 flavors of ice cream, the total number of flavor combinations would be C(5+3-1,3) = C(7,3) = 35.
Similarly, for choosing 10 marbles from a bag with 100 marbles of 3 different colors, we use the same formula. Here, n=3 (three colors) and r=10 (ten marbles) so the total combinations would be C(3+10-1,10) = C(12,10) = 66.
Learn more about Combinations with Repetition