Question:
Everybody in a room shakes hands with everybody else. The total number of handshakes is 45. The total number of persons in the room is
Everybody in a room shakes hands with everybody else. The total number of handshakes is 45. The total number of persons in the room is
Updated On: May 22, 2024
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The Correct Option is B
Solution and Explanation
Number of handshakes = 45
$\Rightarrow \, {^nC_2} = 45$
$ \Rightarrow \, n(n-1) = 90$
$\Rightarrow \, n = 10$
$\Rightarrow \, {^nC_2} = 45$
$ \Rightarrow \, n(n-1) = 90$
$\Rightarrow \, n = 10$
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Concepts Used:
Permutations
A permutation is an arrangement of multiple objects in a particular order taken a few or all at a time. The formula for permutation is as follows:
\(^nP_r = \frac{n!}{(n-r)!}\)
nPr = permutation
n = total number of objects
r = number of objects selected
Types of Permutation
- Permutation of n different things where repeating is not allowed
- Permutation of n different things where repeating is allowed
- Permutation of similar kinds or duplicate objects