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mina [271]
2 years ago
14

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

Mathematics
2 answers:
storchak [24]2 years ago
7 0
<span>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. </span>
slavikrds [6]2 years ago
3 0

There are 6 handshakes between four people in the room.

<h3>Further explanation</h3>

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}} } }

<h2>Permutation ( Arrangement )</h2>

Permutation is the number of ways to arrange objects.

\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }

<h2>Combination ( Selection )</h2>

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}

<h3>Learn more</h3>
  • Different Birthdays : brainly.com/question/7567074
  • Dependent or Independent Events : brainly.com/question/12029535
  • Mutually exclusive : brainly.com/question/3464581

<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Probability

Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation

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