Doubt in Timed Medium Section 2 I Sample#1

GRE Quant Problem Solving
1

Hi!

Doubt in this question:

image
image1325×731 58.1 KB

Here, I was trying to use the 1- unfavourable case method. My logic-

  • Total would be 5 factorial, as 5 different acts.
  • Total unfavourable would be 6- where two singing and 2 dancing are bunched toegther.

Can you please help me understand why this is wrong?

Also I tried to follow the brute force emthod Greg explained in the video- there too my answer is different from the right one. Example, in the first case, where C is left-most, and we arrange the others- the total # cases are explained to be 2. But what is we similarly place C to the right most? That will also produce 2 more cases- making the total cases in this type to be 4.

Can you please guide me on this?
Thanks!

2

You haven’t accounted for the fact that sequences like S_1 S_2 C D_1 D_2 and S_2 S_1 C D_2 D_1 are the “same”. Since the two S’s and two D’s are indistinguishable, the number of unique arrangements is reduced to just \frac{5!}{2! \cdot 2!}= 30.

That looks okay, but there are more exclusions you have to make. For example, something like S_1 S_2 D_1 C D_2 shouldn’t be counted either.

3

Aah! Got my mistakes, thank you so much, extremely useful