You visited us 1 times! Enjoying our articles? Unlock Full Access!

Definition of Function

Let A and B b...

Question

Let $A$ and $B$ be two sets such that $n (A) = 6$ and $n (B) = 3,$ then number of onto functions from $A$ to $B$ is

540.0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

540.00

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

540

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

If $n (A) = m$ and $n (B) = n,$ where $1 \leq n \leq m,$ then number of onto functions from $A$ to $B$
$= n \sum r = 1 (- 1)^{n - r}^{n} C_{r} \cdot r^{m}$

Here, $m = 6, n = 3$
$∴$ Number of onto functions
$= 3 \sum r = 1 (- 1)^{3 - r}^{3} C_{r} \cdot r^{6}$
$=^{3} C_{1} -^{3} C_{2} (2^{6}) +^{3} C_{3} (3^{6})$
$= 3 - 192 + 729$
$= 540$

Suggest Corrections

Similar questions

Let A and B be two sets such that n(A) = p and n(B) = q, write the number of functions from A to B.

A

B

n (A) = p

n (B) = q

A

B

Let A and B be two non empty sets such that $n (A) = 5, n (B) = 6$ and $n (A \cap B) = 3$ .

Find (i) $n (A \times B)$ ,

(ii) $n (B \times A)$ and

(iii) $n (A \times B) \cap (B \times A)$

A & B

n (A) = p

n (B) = q,

A \to B

B \to A

Join BYJU'S Learning Program

Explore more

Join BYJU'S Learning Program