Question

If A and B have 5 and 4 elements respectively, then number of onto functions from A to B is N then
10 equals​

Answer 1

Answer:

Correct option is

D

540

Number of onto functions from A to B if n(A)=m,n(B)=n and

1≤n≤m are equal to

r=1

∑

n

(−1)

n−r

n

C

r

r

m

Here n=3,m=6

∴ Number of onto functions =

r=1

∑

3

(−1)

3−r

3

C

r

r

6

=(−1)

2

3

C

1

1

6

+(−1)

1

3

C

2

2

6

+(−1)

0

3

C

3

3

6

=(3)

6

−3×2

6

+3 =3((3)

5

−2

6

+1)=540

Answer 2

Concept: If number of function in A is n and B is m.

Then,the number of onto functions from A to B = $n^{m}$ – nC1(n-1)m + nC2(n-2)m – nC3(n-3)m+….- nCn-1 (1)m.

Solution:

$4^{5} - 4C1( 3)^{5} +4C3 (2)^{5} -4C3 (1)^{5} +4C4(0)^{5}$

256-972+192-4+0

-528

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