Let m denote the number of ways in which 4 different books are distrib

Question

Let m denote the number of ways in which 4 different books are distributed among 10 persons, each receiving none or one only and let n denote the number of ways of distribution if the books are all alike. Then:

(A) m = 4n
(B) n = 4m
(C) m = 24n
(D) m = 32n
(E) m = 36n

(A) m = 4n 
(B) n = 4m
(C) m = 24n 
(D) m = 32n 
(E) m = 36n

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chetan2u · Answer

Let m denote the number of ways in which 4 different books are distributed among 10 persons, each receiving none or one only and let n denote the number of ways of distribution if the books are all alike. Then:

(A) m = 4n
(B) n = 4m
(C) m = 24n
(D) m = 32n
(E) m = 36n

Let n denote the number of ways of distribution if the books are all alike : Here order does not matter. So we can choose any 4 out of 10 and give them one book each. => n=10C4= \frac{10*9*8*7}{4!}..........4!n=10*9*8*7 ......(II)

From I and II
4!n=24n=m

C

ScottTargetTestPrep · Answer

Solution:
 
The problem can be translated to how many ways can we express 10 as a sum of 4 ones and 6 zeros. Of course, the answer is 10! / (4! x 6!). However, this assumes that the 4 ones (or the 4 books in this case) are indistinguishable (i.e., alike). In other words, n = 10! / (4! x 6!). If the 4 books are different, then we have to multiply 10! / (4! x 6!) by 4! since there are 4! ways rearrange the 4 different books. In other words, m = 4! x   or m = 24n.

Answer: C

flippedeclipse · Answer

The first part is a permutation question, because the books are all different.

m=\frac{10!}{6!}=7*8*9*10

Second part is a combinations question because the books are all the same.

n=10C4=\frac{7*8*9*10}{4*3*2}=3*7*10

m and n differ by a factor of 24, because that is what we divided n by:  4*3*2=24 . The numerator of n was originally identical to m.

Thus, answer is C.

Let m denote the number of ways in which 4 different books are distrib

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GMAT Problem Solving (PS) Questions

Let m denote the number of ways in which 4 different books are distrib

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