At the end of a business conference, the ten people present all shake hands with each other once. How many handshakes will there be altogether?

Question

If \[ \sum_{r=1}^{30} r^2 \left( \binom{30}{r} \right)^2 = \alpha \times 2^{29}, \] then \( \alpha \) is equal to _________.

Answer 1

Step 1: Person 1 shakes hands with the remaining 9 people.

Step 2: Person 2 shakes hands with the remaining 8 new people, having already shaken with person 1, and so on down to person 9 shaking hands with just 1 remaining person.

Step 3: Adding these: \( 9+8+7+6+5+4+3+2+1 = 45 \).
\[ \boxed{45} \]

At the end of a business conference, the ten people present all shake hands with each other once. How many handshakes will there be altogether?

Show Hint

The Correct Option is B

Solution and Explanation

Top Questions on Combinatorics

Questions Asked in SNAP exam