1.2-14 A bag of 36 dum-dum pops (suckers) contains up to 10 flavors. That is, there arefrom 0 to 36 suckers of each of 10 flavors in the bag. How many different flavor combinationsare possible?
Question
1.2-14 A bag of 36 dum-dum pops (suckers) contains up to 10 flavors. That is, there arefrom 0 to 36 suckers of each of 10 flavors in the bag. How many different flavor combinationsare possible?
Solution
This problem is a classic example of a problem in combinatorics known as the "stars and bars" problem.
The problem can be solved by using the formula for combinations with repetition, which is (n + r - 1) choose r, where n is the number of flavors (10) and r is the number of suckers (36).
So, the number of different flavor combinations is (10 + 36 - 1) choose 36 = 45 choose 36.
This is a large number and can be calculated using a calculator or a computer program. The result is 119,759,850.
So, there are 119,759,850 different flavor combinations possible.
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