Question

Six People (four women and two men) arrange themselves randomly in six consecutive seats in a row. Find the probability that the women will be in four adjacent seats. (Hint: The Denominator of the probability of the fraction will be 6=720, the total number of ways to arrange six items.)

Answer 1

The probability that women will be in four adjacent seats is 0.2.

Explanation:

Since six people are there and women will be in four adjacent seats so treating 4 women as a unit.

Now, 2 men and 4 women (1 unit) can be arranged in 3! ways .

The 4 women can be arranged in themselves in 4! ways

so total number of ways = 3!×4!=144

Also the total number of possible arrangement = 6!=720 ways

As per question,

Required Probability=
`(144)/(720)` = 0.2