theGame001
Bunuel, why not this
_ _ _ _ _ _
2*1*4*3*2*1= 48
We are already using 2*1 for FY, if we consider them as one unit and do 5!, wont there be duplication?
Where am I going wrong?
The problem can be divided into 3 sections in order to better the understanding. The word 'Family' has 6 letters and we are asked to keep F and Y together:
a. Listing different possibilities of arranging F and Y
b. Arranging the remaining 4 letters around F and Y
c. Arranging F and Y between themselves
a.The set F and Y can occur in any of the two positions within the 6 positions i.e. 5 ways
F Y _ _ _ _
_ F Y _ _ _
_ _ F Y _ _
_ _ _ F Y _
_ _ _ _ F Y
b.The remaining 4 letters can be arranged in the blank spaces ("_") shown in point a.
F Y
4 3 2 1 \(= 24\)
4 F Y
3 2 1 \(= 24\)
4 3 F Y
2 1 \(= 24\)
4 3 2 F Y
1 \(= 24\)
4 3 2 1 F Y \(= 24\)
c.Finally, F and Y can be arranged in 2 ways i.e F Y and Y F
Combining b and c we get,
\((24*5) * 2 = 240\) (Ans. C)