Question
Rahul has joined Instagram and has 12 friends and each
of these friends has 20 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 Rahul and the maximum number of invitations sent by Rahul.Solution
For minimum number of invitations sent by Rahul,
All of Rahul’s friends need to know each other and their friends should also be the same i.e.
12 friends should be common to each of his friends.
So, minimum number of invitations = 20 For maximum number of invitations sent by Rahul,
Rahul has 12 friends and each of his friends has 20 friends.
So, apart from Rahul, each of the 12 friends has 19 friends each.
As, Rahul’s at least two friends know each other
So, maximum number of invitation (When only two friends know each other)
= (12 × 19 + 12) – 2 = 238
Required difference = 238 − 20 = 218
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