Question

The total number of onto functions from the set {1,2,3,4) to the set (3,4,7) is
A. 18
B. 36
C. 64
D. none of these

Answer 1

Correct Answer - B
If A and B are two sets consisting of m and n elements respectively such that `1 le n le m`, then number of onto functions from A to B is:
`underset(r=1)overset(n)sum(-1)^(n-r) .^(n)C_(r) r^(m)`
Here, m=4 and n=3
So, total number of onto functions.
`underset(r=1)overset(3)sum(-1)^(3-r) .^(3)C_(r) r^(4)`
`^(3)C_(1)-^(3)C_(2)xx2^(4)+^(3)C_(3)xx3^(4)=3-48+81=36`