The number of one-one and onto functions that can be defined from { 1,2,3,4 } onto set  is 24  then n ( B ) is 
  • A
    $$4$$
  • B
    $$2$$
  • C
    $$3$$
  • D
    $$6$$

Solution

Let set A be $${1,2,3,4}$$.
$$n(A ) = 4$$.
Given that number of one to one and onto functions from A to B are 24.
If $$n(B)=4$$,
Number of one to one functions from A to B = $$4!=24$$
No of onto functions =$$0$$   [Since $$n(A)=n(B)$$]
Hence n(B)=$$ 4 $$satisfies the given condition.