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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
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
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
The reason you can't use 5x5x5 is that you will have duplicates. For example: Banana Choc Lemon is essentially the same as Lemon, Choc, Banana and also Choc, Lemon, Banana. So you do not duplicate it's easier to use the 7C3 formula which gives 35 (7!/3!x4!)
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. _________________
Salaries are low in recession. So, working for kudos now.
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.
Agree with the great explanation given. _________________
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 _________________
Salaries are low in recession. So, working for kudos now.
Re: Permutation / combinations [#permalink]
15 Oct 2009, 02:51
The question can be solved with the use of the false coins method.
Now u have three scoops to choose and 5 diff flavours from which to choose from
So u need to put three good coins represented by "O" and 4 false coins represented by "X"
so now we have to arrange these three good coins and 4 false coins
This can be done in 7C3 ways
Now how will this solve the problem
Consider a combination
OOXXOXX
Any "O" left of the first X is the number of scoops of the first flavour = 2 scoops of flavour 1 Any "O" left of second X and right of first X is number of scoops of second flavour = 0 scoops of flavour 2 Similarly any "O" left of third and right of second X is number of scoops of third flavour = 1 scoops of flavour 3 Similarly any "O" left of Fourth and right of third X is number of scoops of fourth flavour = 0 scoops of flavour 4 Now finally any "O" right of fourth X is number of scoops of flavour 5 = 0 scoops of flavour 5 in this case
Similarly we can arrange as XOXOXOX Flavour 1 = 0 Flavour 2 = 1 Flavour 3 = 1 Flavour 4 = 1 Flavour 5 = 0
I hope this helps....
Similarly if there were 4 scoops to choose and 6 flavours the answer would be 9C4 as there would be 5 false coins ("X") and 4 good coins ("O") which we have to arrange.
Re: Permutation / combinations [#permalink]
15 Nov 2013, 05:04
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