Question
Priya has joined Twitter and has 8 friends and each of
these friends has 12 friends. Later, it is found that at least two of her friends know each other and on marriage, she wants to invite all her friends and all the friends of her friends. Find the difference between minimum number of invitations sent by Priya and the maximum number of invitations sent by Priya.Solution
For minimum number of invitations sent by Priya,
All of Priya’s friends need to know each other and their friends should also be the same i.e.
8 friends should be common to each of her friends.
So, minimum number of invitations = 12 For maximum number of invitations sent by Priya,
Priya has 8 friends and each of her friends has 12 friends.
So, apart from Priya, each of the 8 friends has 11 friends each.
As, Priya’s at least two friends know each other
So, maximum number of invitation (When only two friends know each other)
= (8 × 11 + 8) – 2 = 94
Required difference = 94 − 12 = 82
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