Question

Let $A=\{1,2,3\}$ and $B=\{a,b,c\}$, then the number of bijective functions from $A$ to $B$ are

• A. 2
• B. 8
• C. 6
• D. 4

Answer 1

Answer: (C)

Initially when no element of $A$ is mapped with any element of $B$, the element 1 of set $A$ can be mapped with any of the elements a, $b$ and $c$ of set $B$. Therefore 1 can be mapped in 'three' ways. Having mapped 1 with one element of $B$, now we have 'two' ways in which element 2 can be mapped with the remaining two elements of $B$. Having mapped 1 and 2 we have one element left in the set $B$ so there is only 'one' way in which the element 3 can be mapped. Therefore the total number of ways in which the elements of A can be mapped with elements of $B$ in this way are $3\times 2\times 1=6$. Hence the number of bijective functions from $A$ to $B$ are 6 .