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Let A={1,2,3,4,5,6}. If f be a bijective function from A to A, then the no of such functions for which f(k) is not equals to k , where k=1,2,3,4,5,6 is ? Explain pls.

Let A={1,2,3,4,5,6}. If f be a bijective function from A to A, then the no of such functions for which f(k) is not equals to k ,  where k=1,2,3,4,5,6 is ? Explain pls.

Grade:12th Pass

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Aditi,

 

A bijective function is one where it is both one-one and onto.

 

So from the total of 6! ways of bijective functions, one function where,

f(1) = 1 & f(2) = 2 & f(3) = 3 &.......f(6) = 6 has to be removed

 

So total is 6! - 1 = 719 functions.

 

Hope that helps.

 

Best Regards,

Ashwin (IIT Madras).

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