It is combination case, isn't it? but I got 25 ways instead of 35, my process to come to this result as follow, not sure where is it went wrong.
B C L S V
3 0 0 0 0 -->C(5,1)= 5 ways
2 1 0 0 0 -->C(5,2)=10 ways
1 1 1 0 0 -->C(5,3)=10 ways

Question 1
There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be? (flavors cannot be repeated)
Answer
5C3 = 5!/(3! x 2!) = 10

Question 2
There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be? (flavors can be repeated)
Answer
5 x 5 x 5 = 125

Question 3
There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be? (flavors can be repeated but order doesn't matter)
Answer
(5+3-1)! / [3! x (5-1)!] = 35

From GMAT point of view, you need to know only first and second questions.

I am sure, 3rd question is not from any reputed GMAT related material.

There are many things, Permutation with repetition, Permutation without repetition, Combination with repetition, Combination without repetition. GMAT doesn't ask all the things. This will become very very complicated.

Still if u want to do research on question number 3, you can do that (but not for your GMAT exam). This question is about "Combination without repetition". So, here we can do repetitions. But point to be noted is that it is a combination problem. So, order doesn't matter.
Normally, when we take 5^3, order matters. So, BBL and BLB are different possibilities. But in 3rd question, BBL & BLB are same only (because order doesn't matter). This way, we need to proceed.
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the 7 was right. the 5 is wrong. There are 35 combination.

Here is from the original text:

Explanation to the problem:

Combination with repetition:

(n+r-1)! / r!(n-1)!

where n is the number of things to choose from, and you choose r of them
(Repetition allowed, order doesn't matter)

(5+3-1)! / 3!(5-1)! =

7! / 3! x 4! =

5040 / 6 x 24 =

35

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Agree with the great explanation given.
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In GMAT, if this question comes and its not clarified whether the flavors can be repeated or not, then u should assume that flavors can be repeated.
Answer will be 5*5*5 = 125

However, if there are 5 colored balls and we need to choose 3, and nothing is mentioned whether repetition is allowed or not. In that case, u should assume that balls are unique and each colored ball can not be repeated.
Answer will be 5C3 = 10


I think its clear what is the difference between these two examples. So, original question's answer is 125
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Salaries are low in recession. So, working for kudos now.