There are 6 handshakes between four people in the room.
Further explanation
The probability of an event is defined as the possibility of an event occurring against sample space.
\(\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }\)
Permutation ( Arrangement )
Permutation is the number of ways to arrange objects.
\(\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }\)
Combination ( Selection )
Combination is the number of ways to select objects.
\(\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }\)
Let us tackle the problem.
This problem is about Combination.
If there are 4 people in a room , then the number of handshaking between 2 people is analogy as selecting 2 people from 4 people available. We will use combination formula in this problem.
\(^4C_2 = \frac{4!}{2! (4-2)!}\)
\(^4C_2 = \frac{4!}{2! 2!}\)
\(^4C_2 = \frac{4 \times 3 \times 2 \times 1}{2 \times 1 \times 2 \times 1}\)
\(^4C_2 = \frac{ 24 }{4}\)
\(^4C_2 = \boxed{6}\)
Learn more
- Different Birthdays : https://brainly.com/question/7567074
- Dependent or Independent Events : https://brainly.com/question/12029535
- Mutually exclusive : https://brainly.com/question/3464581
Answer details
Grade: High School
Subject: Mathematics
Chapter: Probability
Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation
