Let $A$ and $B$ be two sets such that $n (A) = 6$ and $n (B) = 3.$ If $x$ denotes the number of onto functions from $A$ to $B$ and $y$ denotes the number of one-one functions from $B$ to $A,$ then the value of $x - y$ is equal to

Open in App

Solution

Given $n (A) = 6, n (B) = 3$
$x =$ Number of onto functions from $A$ to $B$
$=^{3} C_{0} \cdot 3^{6} -^{3} C_{1} \cdot 2^{6} +^{3} C_{2} \cdot 1^{6} = 540$
$y =$ Number of one-one functions from $B$ to $A$
$=^{6} P_{3} = 120$
$∴ x - y = 420$

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.

Q. Let A and B be any two sets such that n(A) = p and n(B) = q, then the total functions from A to B is equal to __________ .

Q. Let

A

and

B

be any two sets such that

n (A) = p

and

n (B) = q

, then the total number of functions from

A

B

is equal to

Q. Let

A

and

B

be two sets such that

n (A) = 6

and

n (B) = 3,

then number of onto functions from

A

B

Let $x$ denote the total number of one-one functions from a set $A$ with $3$ elements to a set $B$ with $5$ elements and $y$ denote the total number of one-one functions from the set $A$ to the set $A \times B$ . Then

Join BYJU'S Learning Program

Let A and B be two sets such that n(A)=6 and n(B)=3. If x denotes the number of onto functions from A to B and y denotes the number of one-one functions from B to A, then the value of x−y is equal to

Given n(A)=6,n(B)=3 x= Number of onto functions from A to B =3C0⋅36−3C1⋅26+3C2⋅16=540 y= Number of one-one functions from B to A =6P3=120 ∴x−y=420

Let $A$ and $B$ be two sets such that $n (A) = 6$ and $n (B) = 3.$ If $x$ denotes the number of onto functions from $A$ to $B$ and $y$ denotes the number of one-one functions from $B$ to $A,$ then the value of $x - y$ is equal to

Given $n (A) = 6, n (B) = 3$
$x =$ Number of onto functions from $A$ to $B$
$=^{3} C_{0} \cdot 3^{6} -^{3} C_{1} \cdot 2^{6} +^{3} C_{2} \cdot 1^{6} = 540$
$y =$ Number of one-one functions from $B$ to $A$
$=^{6} P_{3} = 120$
$∴ x - y = 420$