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  • Number of ways in which a matrix match arrangement of order 5*5 with one to one correspondence can be attempted such that none of the part is correctly matched is<s

Number of ways in which a matrix match arrangement of order 5*5 with one to one correspondence can be attempted such that none of the part is correctly matched is

Option: 1

41 


Option: 2

42 


Option: 3

43 


Option: 4

44 


Answers (1)

best_answer

As we have learned

If n things are arranged in a row, the number of ways in which they can be arranged, so that none of them occupies its correct place is =n! \left(1-\frac{1}{1!}+\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!}+...+(-1)^{n}{\frac{1}{n!}} \right ).

 

Now,

Clearly, number of ways = D(5) = 5 ! \left ( 1- \frac{1 }{1!}+ \frac{1}{2!}- \frac{1 }{3!}+ \frac{1}{4!}-\frac{1}{5!} \right )= 60 -20 +5 -1 = 44

Posted by

Sumit Saini

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