Question

11. If six persons sit around a table, the probability that some specified three of them are always
together is
a)1/20
b)3/10
c)1/5
d)4/5​

Answer 1

Answer:

Explanation:

Concept: Probability is a way of measuring the likelihood that something will happen. Many things are difficult to predict with absolute certainty. With its help, we can only predict how likely an event is to happen, or its probability of happening. The probability can range from 0 to 1, with 0 indicating impossibility and 1 indicating certainty. For 10th graders, the probability is a key subject as it teaches all the basic ideas of the subject. One is the probability of each event in the sample space.

Given: six people are sitting around a table

Find: the probability that a certain three of them are always together

Solution:

6 people can sit around the table at 5! ways

Considering three persons sitting together as 1 unit

Now there are 3 + 1 = 4 entities

These 4 entities can be arranged in 3! ways

In the entities themselves, they can be arranged in 3! ways

Required number of arrangements = 3! 3!

$probability=\frac{m}{n}=\frac{3!3!}{5!} =\frac{6}{20}=\frac{3}{10}$

Hence the probability that some specified three of them are always together will be 3/10.

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