Question

Q.'7' persons are seated on '7' chairs around a table. The probability that three specified persons are always sitting next to each other is:
(a)1/4
(b)1/5
(c) 1/6
(d) 1/3
a​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

The probability of the 3 specified persons to always sit next to each other is $\frac{1}{5}$.

Hence, option b) 1/5 is the correct option.

Step-by-step explanation:

Given,

• 7 persons are seated on 7 chairs around a table.

To find:

• The probability that three specified persons are always sitting next to each other =?

Total number of possible sitting arrangements = $\frac{7{\displaystyle !\,}}{7}$ = $6{\displaystyle !\,}$

Let the three specified persons as one entity = A = 1

Now,

• The entities are 7 - 3 + A = 4 + 1 = 5

Then,

• The sitting arrangements become = $\frac{5{\displaystyle !\,}}{5}$ = $4{\displaystyle !\,}}$

Now,

The three specified persons can interchange their places in $3{\displaystyle !\,}$ ways.

Therefore,

• Number of favourable sitting arrangements are = $4{\displaystyle !\,}} 3{\displaystyle !\,}}$

As we know,

• Probability = $\frac{m}{n}$

Here,

• m = Number of favourable outcomes
• n = The total outcomes

Hence,

• Probability = $4{\displaystyle !\,}} 3{\displaystyle !\,}} / 6{\displaystyle !\,}}$
• Probability = $\frac{1}{5}$

Therefore, the probability that three specified persons are always sitting next to each other = $\frac{1}{5}$.