Accepted 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: ABACADBCBDCD There are no other combinations.
Suggested Answer
There are 6 handshakes between four people in the room.Further explanationThe 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 moreDifferent Birthdays : https://brainly.com/question/7567074Dependent or Independent Events : https://brainly.com/question/12029535Mutually exclusive : https://brainly.com/question/3464581Answer detailsGrade: High SchoolSubject: MathematicsChapter: ProbabilityKeywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation
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