Permutation / combinations

[benjiboo]

There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be?






Why is the answer 35 (7!/3!x4!) and not 5^3 written like (5*5*5)=125?

Thank you

[vivekjaiswal]

I would have gone for the 5*5*5
But as you say it isn't the right answer...I hope someone would clarify

I hope there isn't anything missing in the question

[benjiboo]

I would have gone for the 5*5*5
But as you say it isn't the right answer...I hope someone would clarify

I hope there isn't anything missing in the question

Nothing is missing in the question. Someone needs to clarify why you can not use the 5*5*5 formula. (n^r)

[Trader AK]

There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be?

Why is the answer 35 (7!/3!x4!) and not 5^3 written like (5*5*5)=125?

Thank you

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.

[rajiishere]

I would have gone for 5*5*5 or would have thought that something on the question about repetition is missing...

But Trader AK, that was a detailed explanation...Thanks!

[benjiboo]

Trader AK, thank you for the explanation.

[vivekjaiswal]

There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be?

Why is the answer 35 (7!/3!x4!) and not 5^3 written like (5*5*5)=125?

Thank you

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.

Hi Trader AK,

Thanks for showing us all the possible outcomes of various interpretations.
May be I am being really dumb, but could you please also explain how you arrived at the last expression (the one I have bold faced in the quote above.)

Thanks Again,
Vivek