Q.

A set A contains 10 elements. A function from A to itself is formed. The probability that the function so formed is not on-to is

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a

10109

b

19(109)

c

10(10)10

d

1109

answer is D.

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Detailed Solution

The number of onto functions from A to itself is =10

n(S)=1010

n(A)=10!

P(A)=n(E)n(S)=101010

P(A¯)=1P(A)

=1101010

=110×9!1010

=19!109

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A set A contains 10 elements. A function from A to itself is formed. The probability that the function so formed is not on-to is