Let m , n be positive integers with m n . Match the counts. Column I: (A) Distribute m distinct books among n children. (B) Arrange n distinct books in m places. (C) Select m people from n excluding

Question

Let m , n be positive integers with m > n . Match the counts. Column I: (A) Distribute m distinct books among n children. (B) Arrange n distinct books in m places. (C) Select m people from n excluding two particular people. (D) Distribute m distinct books among n children with each child receiving at least one. Column II: (p) 0 (q) ( m − n m − 1 ​ ) m ! ( r ) n m ( s ) ( n m ​ ) n ! Column I Column II (A) Distribute m distinct books among n children. (p) 0 (B) Arrange n distinct books in m places. (q) ( m − n m − 1 ​ ) m ! (C) Select m people from n excluding two particular people. (r) n m (D) Distribute m distinct books among n children with each child receiving at least one. (s) ( n m ​ ) n !

TestHub · Accepted Answer

A has n m assignments, B has m ! / ( m − n )! injections, and C is impossible since m > n . D is the onto-function count n ! S ( m , n ) = ∑ j = 0 n ​ ( − 1 ) j ( j n ​ ) ( n − j ) m , which is not any listed expression in general. Note: D has no listed expression in Column II; D maps to the leftover option (q) by elimination.

Column I	Column II
(A) Distribute $m$ distinct books among $n$ children.	(p) 0
(B) Arrange $n$ distinct books in $m$ places.	(q) $(m - n m - 1) m!$
(C) Select $m$ people from $n$ excluding two particular people.	(r) $n^{m}$
(D) Distribute $m$ distinct books among $n$ children with each child receiving at least one.	(s) $(n m) n!$

Mathematics - Permutation & Combination Question with Solution | TestHub

Options:

Doubts & Discussion