Answer :

The correct answer is 6.

The clearest way to determine this is by creating a table of possible hand shaking. If we label the people A-D, the following are the ways they can be combined:
AB
AC
AD
BC
BD
CD

There are no other combinations.

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.

[tex]\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }[/tex]

Permutation ( Arrangement )

Permutation is the number of ways to arrange objects.

[tex]\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }[/tex]

Combination ( Selection )

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]

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

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