Question:

Three married couples are to be seated in a row having six seats in a cinema hall. If spouses are to be seated next to each other, in how many ways can they be seated? Find also the number of ways of their seating if all the ladies sit together.

Updated On: Jul 7, 2022
  • $ 40,140 $
  • $ 48,144 $
  • $ 45,142 $
  • $42,140 $
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is B

Solution and Explanation

Let us denote married couples by $S_1, S_2, S_3$, where each couple is considered to be a single unit as shown in the following figure:
Then the number of ways in which spouses can be seated next to each other is $3! = 6$ ways. Again each couple can be seated in $2!$ ways. Thus the total number of seating arrangement so that spouses sit next to each other $= 3! \times 2! \times 2! \times 2! = 48$ Again, if three ladies sit together, then $3$ ladies can be taken as one unit. Therefore, the total number of ways where ladies sit together is $4! \times 3! = 144$.
Was this answer helpful?
0
0

Top Questions on Straight lines

View More Questions

Notes on Straight lines

Concepts Used:

Straight lines

A straight line is a line having the shortest distance between two points. 

A straight line can be represented as an equation in various forms,  as show in the image below:

 

The following are the many forms of the equation of the line that are presented in straight line-

1. Slope – Point Form

Assume P0(x0, y0) is a fixed point on a non-vertical line L with m as its slope. If P (x, y) is an arbitrary point on L, then the point (x, y) lies on the line with slope m through the fixed point (x0, y0) if and only if its coordinates fulfil the equation below.

y – y0 = m (x – x0)

2. Two – Point Form

Let's look at the line. L crosses between two places. P1(x1, y1) and P2(x2, y2)  are general points on L, while P (x, y) is a general point on L. As a result, the three points P1, P2, and P are collinear, and it becomes

The slope of P2P = The slope of P1P2 , i.e.

\(\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}\)

Hence, the equation becomes:

y - y1 =\( \frac{y_2-y_1}{x_2-x_1} (x-x1)\)

3. Slope-Intercept Form

Assume that a line L with slope m intersects the y-axis at a distance c from the origin, and that the distance c is referred to as the line L's y-intercept. As a result, the coordinates of the spot on the y-axis where the line intersects are (0, c). As a result, the slope of the line L is m, and it passes through a fixed point (0, c). The equation of the line L thus obtained from the slope – point form is given by

y – c =m( x - 0 )

As a result, the point (x, y) on the line with slope m and y-intercept c lies on the line, if and only if

y = m x +c