Question
Nikhil has joined Facebook and has 18 friends and each
of these friends has 25 friends. Later, it is found that at least two of his friends know each other and on marriage, he wants to invite all his friends and all the friends of his friends. Find the difference between minimum number of invitations sent by Nikhil and the maximum number of invitations sent by Nikhil.Solution
For minimum number of invitations sent by Nikhil,
All of Nikhil’s friends need to know each other and their friends should also be the same i.e.
18 friends should be common to each of his friends.
So, minimum number of invitations = 25 For maximum number of invitations sent by Nikhil,
Nikhil has 18 friends and each of his friends has 25 friends.
So, apart from Nikhil, each of the 18 friends has 24 friends each.
As, Nikhil’s at least two friends know each other
So, maximum number of invitation (When only two friends know each other)
= (18 × 24 + 18) – 2 = 448
Required difference = 448 − 25 = 423
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