theGame001
The number of ways that 5 Marathi, 3 English and 3 Tamil books be arranged if the books of each language are to be kept together are...
(A) 5920
(B) 25920
(C) 9250
(D) 7480
OA: not available
Source: foundation book
Dear
theGame001I'm happy to help.
This doesn't really look like a GMAT Quant question because (a) it only has four answers; (b) the answers are not in numerical order; (c) the numbers are a bit bigger than the GMAT expects folks to do without a calculator; and (d) the question is not completely unambiguous. I would not recommend relying on questions from this source to prepare you adequately for the GMAT.
For the math behind these calculations, see:
https://magoosh.com/gmat/2012/gmat-permu ... binations/https://magoosh.com/gmat/2012/gmat-math- ... binations/https://magoosh.com/gmat/2012/gmat-factorials/https://magoosh.com/gmat/2012/gmat-quant-how-to-count/I will assume what they mean is that we could have the three groups ---- (5 Marathi books) and (3 English books) and (3 Tamil books) in any order. That's a set of three, which can be arranged in 3! = 6 ways.
Within the 5 Marathi books, there are 5! = 120 orders.
Within the 3 English books, there are 6! = 6 orders.
Within the 3 Tamil books, there are 6! = 6 orders.
The Fundamental Counting Principle tells us to multiply all these:
total = 120*6*6*6 = 25,920
Answer =
(B)Does all this make sense?
Mike