MATHEMATICS HIGH SCHOOL

Four people in a room. Each shakes hands with each of the others once. How many handshakes are there? 6
10
12
16
22

Answers

Answer 1
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.
Answer 2
Answer:

There are 6 handshakes betweenfour 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 = (n!)/((n - r)!) } }

Combination ( Selection )

Combination is the number of ways to select objects.

\large {\boxed {^nC_r = (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 = (4!)/(2! (4-2)!)

^4C_2 = (4!)/(2! 2!)

^4C_2 = (4 * 3 * 2 * 1)/(2 * 1 * 2 * 1)

^4C_2 = ( 24 )/(4)

^4C_2 = \boxed{6}

Learn more

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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