Find the number of ways in which four men, two women and a child can sit at a table if the child is seated between two women.

A. 24
B. 36
C. 48
D. 120
E. 240

Please help me with this question?

Question

Find the number of ways in which four men, two women and a child can sit at a table if the child is seated between two women.

A. 24
B. 36
C. 48
D. 120
E. 240

Please help me with this question?

Krishna kumar · Accepted Answer

We start by seating the child between the two women. There are two possible arrangements for this:
Woman 1 - Child - Woman 2Woman 2 - Child - Woman 1So, there are 222 ways to arrange the two women and the child.
Since the group of two women and one child must sit together in the lineup, we treat them as a single "block" or "super person". This "block" can be seated in any of the 555 remaining slots when considering the four men, giving us 555 positions for the "block".
Next, we need to arrange the four men and the "block" (with the child and women already fixed in one of their two arrangements). There are 5!5!5! (factorial) ways to arrange these 5 "people" in the seats:
5!=1205! = 1205!=120
Finally, multiply the number of ways to arrange the women and child (2 ways) by the number of ways to position the "block" and arrange the other men (120 ways):
2&times;120=2402 	imes 120 = 2402&times;120=240
Final Answer : There are 240 ways to seat the four men, two women, and a child at the table with the child seated between two women.

Find the number of ways in which four men, two women and a child can sit at a table if the child is seated between two women. A. 24 B. 36 C. 48 D. 120 E. 240 Please help me with this question?