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  4. In a group of 6 people, each person sends an email and receives an email amongst themselves. The different number of ways of doing this is N then the last digit of N is (if it is given that no one sends email back to himself)

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Q. In a group of $6$ people, each person sends an email and receives an email amongst themselves. The different number of ways of doing this is $N$ then the last digit of $N$ is (if it is given that no one sends email back to himself)

NTA AbhyasNTA Abhyas 2022

Solution:

Number of ways
$=6!\left(\frac{1}{2 !} - \frac{1}{3 !} + \frac{1}{4 !} - \frac{1}{5 !} + \frac{1}{6 !}\right)$
$=265$