Chapter 11.6, Problem 39E

a.

To determine

To calculate: thepossibilities of seating arrangement of two man and two women if a man sits first .

Answer to Problem 39E

Number of arrangements if man sits first is $4$ .

Explanation of Solution

Given :

No of mans = two

No of women = two

No man is sitting next to another man and no women is sitting next to the another women.

Calculation :

If man sits first then there is two possibilities for first seat then there is two possibilities for second seat because there is two women and after that there is only one-one possibilities left for the next two seats. For arrangement multiply these possibilities,

  $2·2\cdot 1\cdot 1=4\text{ [multiply]}$

Hence,Number of arrangements if man sits first is $4$ .

b.

To determine

To calculate: the possibilities of seating arrangement of two man and two women if a women sits first .

Answer to Problem 39E

Number of arrangements if women sits first is $4$ .

Explanation of Solution

Given :

No of mans = two

No of women = two

No man is sitting next to another man and no women is sitting next to the another women.

Calculation :

If woman sits first then there is two possibilities for first seat then there is two possibilities for second seat because there is two women and after that there is only one-one possibilities left for the next two seats. For arrangement multiply these possibilities,

  $2·2\cdot 1\cdot 1=4\text{ [multiply]}$

Hence, Number of arrangements if women sits first is $4$ .

c.

To determine

To calculate: the possibilities of seating arrangement of two man and two women if a man sits and woman sits altogether.

Answer to Problem 39E

When altogether the total arrangements is $8$ .

Explanation of Solution

Given :

No of mans = two

No of women = two

No man is sitting next to another man and no women is sitting next to the another women.

Calculation :

Altogether arrangement = $4+4\text{ [add]}$

  = $8$

When altogether the total arrangementsis $8$ .