MGMAT Guide 4 pg 75

[shoumik]

Hi I have a question on #6 on page 75:

I tried to solve the question using anagram but could not arrive at the same result as the solution.

I solved it as following:
3 male dolphins and 3 female dolphins: AAABBB
Therefore, 6!/3!*3! = 20 which is wrong.

[jlucero]

A good way to double-check the anagram method is to think about how many possible letters could start the word that you're trying to make. In this instance, only 3 dolphins can be first. The anagram would be more like: ABCXYZ where ABC need to be the first three letters and XYZ need to be the last three. Instead of thinking this in terms of one anagram, think of it as two independent anagrams: how many ways can you rearrange ABC? (6) How many ways can you rearrange XYZ? (6) How many ways can you attach these two arrangements together? (36)

As a side note- your answer of 20 would answer a different question: if I rearranged your anagram (AABBAB or ABABAB) I would learn that there are 20 different ways to rearrange the order of dolphins in terms of males and females(6!), if I don't count the unique arrangements of males (divide by 3!) or females (divide by another 3!).

[shoumik]

Thanks for your time Joe but I am having trouble understanding the concept you are trying to explain. How would we solve this with the slot machine method? Furthermore, if we turn to pg185, and compare the method of SSSEEE, how is that situation different from Dolphins situation?

Thanks.

[tim]

you wouldn't solve this with the slot method! the slot method would allow any of the dolphins in any of the positions, which is clearly not allowed in this problem. please re-read Joe's solution and let us know if you have any more questions about that one. keep in mind it is good to have multiple approaches to a problem, but you can't just choose a random strategy and expect it to work on every problem.. :)