aashigarg wrote:
(BR) (1 2 3 )
Let us take BR to be one unit.
Thus number of arrangements = 4!
Also, since B has to be on the left of R it cannot be arranged in 2! ways internally.
Thus IMO - Ans = 24
What am I doing wrong over here?
You're answering a different question from the one in this thread - you're solving the problem "in how many ways can the five people B, R, X, Y and Z be arranged in a row if B must be immediately to the left of R?" The answer to that question is 24, as you solved above.
The question in this thread is different for two reasons: here we only have two people, B and R, and the other three chairs are empty. So we're really arranging these letters: B, R, E, E, E, where "E" represents an empty seat. And in this question, B needs to be somewhere to the left of R, but there might be empty seats between them, so we don't want to think of them as a single unit "BR".
The answer to the problem is small enough that it's not too bad to just list all the possibilities, and if my explanation above is unclear, this should illustrate what's going on - if you do that systematically, you'll get the answer 10:
BREEE
BEREE
BEERE
BEEER
EBREE
EBERE
EBEER
EEBRE
EEBER
EEEBR
though there are much faster ways to answer the question, of course.
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