Question

Three married couples arrange themselves randomly in six consecutive seats in a row. Find the probability that each woman will sit immediately to the left of her husband. The denominator of the probability fraction will be 6! = 720, the total number of ways to arrange six items.

Answer 1

Answer:

1/120

Explanation:

The numerator of the probability fraction will be the number of ways to arrange 3 items: 3!  = 6. So the probability fraction is ...

... 6/720 = 1/120

_____

The 3 items are the three married couples with the woman on the left.

Answer 2

Answer:

The probability that each woman will sit immediately to the left of her husband is 0.1.

Step-by-step explanation:

Given : Three married couples arrange themselves randomly in six consecutive seats in a row.

To find : The probability of the event of the women being in three adjacent seats, as well as the men.

Solution :

There are 2 sets of 3 consecutive seats in a row of 6 seats

The women can be arranged in 3! ways in their three seats

The men can be arranged in 3! ways in their three seats.

The number of ways to succeed is

$n= 2\times 3!\times 3! \\n= 2\times 6\times 6 \\n= 72$

The probability that each woman will sit immediately to the left of her husband is

$P(n)=\frac{n}{6!}\\\\P(n)=\frac{72}{720}\\\\P(n)=\frac{1}{10}\\\\P(n)=0.1$

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The probability that each woman will sit immediately to the left of her husband is 0.1.