Let A = 1,2,3,....., n and B = a,b,c then the number of functions from A to B that are onto is

Question

Let A = 1,2,3,....., n and B = a,b,c then the number of functions from A to B that are onto is (A) 3n - 2n (B) 3n - 2n -1 (C) 3 (2n - 1) (D) 3n - 3(2n - 1)

Tardigrade Admin · Accepted Answer

Number of onto functions: If A B are two sets having m n elements respectively such that 1 le n le m then number of onto functions from A to B is ∑nr-1(-1)n-r .nCr rn Given A = 1,2,3,---- n B= a,b,c ∴ Number of onto functions =∑ 3r-1(-1)3-r .3Cr rn =3C1-3C2 2n+3C3 3n =(3!/2!1!)-(3!/2!1!) 2n +(3!/3!0!)3n =3-3.2n+3n =3n-3(2n-1)

Q. Let $A = {1, 2, 3, ....., n}$ and $B = {a, b, c}$ , then the number of functions from $A$ to $B$ that are onto is

$3^{n} - 2^{n}$

$3^{n} - 2^{n} - 1$

$3 (2^{n} - 1)$

$3^{n} - 3 (2^{n} - 1)$

Q. Let A={1,2,3,.....,n} and B={a,b,c}, then the number of functions from A to B that are onto is

3n−2n

3n−2n−1

3(2n−1)

3n−3(2n−1)

Q. Let $A = {1, 2, 3, ....., n}$ and $B = {a, b, c}$ , then the number of functions from $A$ to $B$ that are onto is

$3^{n} - 2^{n}$

$3^{n} - 2^{n} - 1$

$3 (2^{n} - 1)$

$3^{n} - 3 (2^{n} - 1)$