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Every two persons shakes hands with each other in a party and the total number of hand shakes is 66. The number of guests in the party is
- a)11
- b)12
- c)13
- d)14
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Every two persons shakes hands with each other in a party and the tota...
Let the number of people be x
For a hand shake we need 2 people so selecting 2 person form x can be done in xC2 ways.
Therefore xC2=66
x!/(x-2)!2!=66
x(x-1)/2=66
x(x-1)=132
Solving this we get x=12
So there must be 12 persons in the party.
Most Upvoted Answer
Every two persons shakes hands with each other in a party and the tota...
Given: Total number of handshakes = 66
To find: Number of guests in the party
Let the number of guests be n.
Each person shakes hands with (n-1) other persons (as he cannot shake hands with himself).
Therefore, the total number of handshakes will be:
nC2 = (n*(n-1))/2
Given that this is equal to 66, we can write:
(n*(n-1))/2 = 66
n*(n-1) = 132
n^2 - n - 132 = 0
Solving this quadratic equation, we get:
n = 12 or -11
Since the number of guests cannot be negative, the answer is n = 12.
Therefore, there were 12 guests in the party.
To find: Number of guests in the party
Let the number of guests be n.
Each person shakes hands with (n-1) other persons (as he cannot shake hands with himself).
Therefore, the total number of handshakes will be:
nC2 = (n*(n-1))/2
Given that this is equal to 66, we can write:
(n*(n-1))/2 = 66
n*(n-1) = 132
n^2 - n - 132 = 0
Solving this quadratic equation, we get:
n = 12 or -11
Since the number of guests cannot be negative, the answer is n = 12.
Therefore, there were 12 guests in the party.
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