Let $E = {1, 2, 3, 4}$ and $F = {1, 2},$ then the number of onto functions from $E$ to $F$ is

Open in App

Solution

$E = {1, 2, 3, 4}$ and $F = {1, 2},$
If $n (E) = m$ and $n (F) = n,$ where $1 \leq n \leq m,$ then number of onto functions from $A$ to $B$
$= n^{m} - (^{n} C_{1} (n - 1)^{m} -^{n} C_{2} (n - 2)^{m} + \dots)$
$(∵ m = 4, n = 2, m > n)$
$= 2^{4} - (^{2} C_{1} (2 - 1)^{4})$
$= 16 - 2 = 14$

Suggest Corrections

Similar questions

E = {1, 2, 3, 4}

F = {1, 2}

E

F

E = {1, 2, 3, 4}

F = {1, 2}

Join BYJU'S Learning Program

Explore more

Join BYJU'S Learning Program