Everyone present at a party shakes hands with each other. If the total number of handshakes is 66, how many people were present at the party?

Question: Everyone present at a party shakes hands with each other. If the total number of handshakes is 66, how many people were present at the party?

Solution:
ধরি, পার্টিতে মোট x জন লোক উপস্থিত ছিল।

যেহেতু করমর্দন করতে দুইজন লোকের প্রয়োজন হয়, তাই মোট করমর্দন সংখ্যা = ^xC₂
= x!/{2!(x - 2)!}
= {x(x - 1)(x - 2)!}/{2!(x - 2)!}
= x(x - 1)/2
= (x² - x)/2

প্রশ্নমতে,
(x² - x)/2 = 66
⇒ x² - x - 132 = 0
⇒ (x - 12)(x + 11) = 0
∴ x = 12 or x = - 11

কিন্তু, x = - 11 হতে পারে না।
∴ x = 12