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djdylan2000

A= {1,2,3,4}

B={1,2,3}

What is max no of onto functions from A to B. (Give the working)

pink_ele

every ele of b has pre image in a=>
a single element of A can be related to that of B in...2^3-1 ways
i.e=7 ways
simalarly for all four elements
so total no of funtions=7^4

v22

Q A= {1,2,3,4} B={1,2,3} What is max no of onto functions from A to B. (Give the working)

ans . total no of functions possible from A to B =

but this also includes those functions in which 2 required images are left out + 1 required image if left out !

those functions in which 2 required images are left out = 3C1 x 1 x 1 x 1 x 1 = 3 --------------- (1)

those functions 1 required image if left out = 3C2 x 2 x 2 x 2 x 2 = 16 x 3 = 48 --------------- (2)

but (2) already includes case (1)

total no of required functions = 81 - 48 = 36

djdylan2000

Sorry ans is 36

options were:

18

36

64

None of the above

The Question is from 'Mathematics Spectrum, Arihant' May 2008 problem 15 on page 9

muskaanrelhan

I think @v22 is right...

cz Total no. of functions frm A to B= n(B)^n(A)

which is

ankurgupta91

total no. of functions = 3^4

general formula 4 calculating onto functions
= r^n - rC1 (r-1)^n + rC2 (r-2)^n -...............

nw here, no. of elements in set B = r = 3
nd no. of elements in set A = n = 4

so , total no of onto functions

= 3^4 - 3C1 (2)^4 + 3C2 (1)^4
= 36

thats the answer
hope u gt it ............

djdylan2000

Thanks ankurgupta91

But how did u get that formula? What is the concept behind the formula?

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