Question
Dev has joined Snapchat and has 20 friends and each of
these friends has 40 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 Dev and the maximum number of invitations sent by Dev.Solution
For minimum number of invitations sent by Dev,
All of Dev’s friends need to know each other and their friends should also be the same i.e.
20 friends should be common to each of his friends.
So, minimum number of invitations = 40 For maximum number of invitations sent by Dev,
Dev has 20 friends and each of his friends has 40 friends.
So, apart from Dev, each of the 20 friends has 39 friends each.
As, Dev’s at least two friends know each other
So, maximum number of invitation (When only two friends know each other)
= (20 × 39 + 20) – 2 = 798
Required difference = 798 − 40 = 758
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