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Question

The total number number of ways in which all the digits of the number 79853 can be arranged such that no digit will occur in its original position as given in the number is 


Solution

Given number is 79853
Number of digits is 5
Here, we need to calculate D5
as we know that Dn=n!(111!+12!13!+.....(1)n1n!)
Hence, number of derangements D5=5!(111!+12!13!+14!15!)
D5=120×(11+1216+1241120)
D5=6020+51
D5=44

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