There are 6 handshakes between four people in the room.
The probability of an event is defined as the possibility of an event occurring against sample space.
[tex]\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }[/tex]
Permutation is the number of ways to arrange objects.
[tex]\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }[/tex]
Combination is the number of ways to select objects.
[tex]\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }[/tex]
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.
[tex]^4C_2 = \frac{4!}{2! (4-2)!}[/tex]
[tex]^4C_2 = \frac{4!}{2! 2!}[/tex]
[tex]^4C_2 = \frac{4 \times 3 \times 2 \times 1}{2 \times 1 \times 2 \times 1}[/tex]
[tex]^4C_2 = \frac{ 24 }{4}[/tex]
[tex]^4C_2 = \boxed{6}[/tex]
Grade: High School
Subject: Mathematics
Chapter: Probability
Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation
