How many ways?
Probability
Level
2
In how many ways can 5 men and 3 women be seated in a row of seats if the men are to be seated in consecutive seats?
The answer is 2880.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Analysis. At first, think of the men as if tied together, giving 4 things for arrangement, the men as a unit and 3 women.Then, to seat them we may proceed as follows:
(a) Choose seats for the 3 women and the “unit” of men.
(b) Seat the 5 men in the 5 seats chosen for them.
The number of ways of performing (a) is 4 ! ways and (b) is 5 ! ways, and for (a) and (b) is ( 4 ! ) ( 5 ! ) = 2 8 8 0 ways