Asha has joined LinkedIn and has 10 friends and each of these friends has 15 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 Asha and the maximum number of invitations sent by Asha.

For minimum number of invitations sent by Asha,
All of Asha’s friends need to know each other and their friends should also be the same i.e.
10 friends should be common to each of her friends.
So, minimum number of invitations = 15 For maximum number of invitations sent by Asha,
Asha has 10 friends and each of her friends has 15 friends.
So, apart from Asha, each of the 10 friends has 14 friends each.
As, Asha’s at least two friends know each other
So, maximum number of invitation (When only two friends know each other)
= (10 × 14 + 10) – 2 = 148
Required difference = 148 − 15 = 133