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There are 7 friends (A1, A2, A3....,A7). If A1 have to shake hand with all without repeat. How many hand shakes possible?

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TCS Other Question

33 people {a1, a2, ....a33} meet and shake hands in a circular fashion. In other words, there are totally 33 handshakes involving the pairs, {a1,a2},{a2,a3},....,{a32,a33},{a33,a1}. Then the size of a smallest set of people such that the rest have shaken hands with at least one person in the set is
a. 10 b. 11 c. 16 d. 12
The difference between the ages of two of my three grandchildren is 3. My eldest grandchild's age is three times than the age of my youngest grandchild and my eldest grandchild's age is two years more than the ages of my two youngest grandchildren added together. How old is my eldest grandchild?
15
12
13
10