Question

In: Statistics and Probability

Suppose that four women and two men enter a restaurant and sit at random around a...

Suppose that four women and two men enter a restaurant and sit at random around

a table that has four chairs on one side and another four on the other side. What is

the probability that the men are not all sitting on one side?

Expert Solution

Solution :-

Here we have to find out the probability that the men are not all sitting on one side.

i.e, Required probability = .

Here, N = Total favorable outcomes that the men are not all sitting on one side

N(A) = Total outcomes of men and women sit at random round a table.

From given data , we know that, there are four women and two men enter a restaurant and sit at random around a table that has four chairs on one side and another four on the other side.

i.e, Number of chairs, n = 8 and Number of people,r = 6

Then we get, $N = n_{P}_{r}$

$N = 8_{P}_{6}$

Here, we have four chairs on one side, i.e r = 4 and total number of people (Men + women) is 6. i.e, n = 6. Then in $6_{P}_{4}$ ways 4 people randomly sit on one side.

Here we know the counting principle, i.e, If set A contains 'n' elements and set B contains 'm' elements, there are 'nm' ways". By using this principle we can obtain the total possible outcomes that men are not all sitting on one side is as

$N(A) = 8 * 4 * 6_{P}_{4}$

Then, Required probability =

Required probability = 0.571

Required probability = 0.571

orchestra answered 2 years ago

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