Forum Quiz PM
Joined: 02 Oct 2020
Posts: 57
Given Kudos: 80
Concentration: Strategy, General Management
Re: A photographer is to take group photographs of a class of students for
[#permalink]
20 May 2021, 01:36
I went down the wrong path thinking I'd calculate the total possibilities and subtract out the possibilities where 2 Boys come together or 2 Girls come together. I stumbled upon the right answer anyway because of ball parking, In hindsight I'd suggest using the methods shown above but I'll share what I did just in case it helps.
so first off, 4 G and 4 B. So total 8 people.
Selecting 5 from 8 and where arrangement matters, is \(8P5\) or\( 8C5! * 5!\)
= \(\frac{8!}{3!} = 8*7*6*5*4= 40 * 7 * 24 = 280 * 24\)
Now we know we need to remove the occurrences where BB _ _ _ or GG _ _ _ or both BB GG _
First case, \(2C1 * 4C2 * 4! \)(Selecting either B or G , Selecting 2 from 4 , arranging the grouped 2 , and the rest)
\(=2* 6 * 120 = 1440\)
The other case will definitely be significantly lower than this.
Now looking at the options I Know Option A, C and E are out. Judging by the magnitude, I'd also fairly assume Option B is out and came to the solution of Option D.
Of course, none of these issues would occur if I had not gone down the wrong rabbit hole but hey, here's a not so bad to get out of it in time.