Seating Arrangements at a Theater In Exercises 65-68, Artie, Bobbette, Chuck, Deirdre, Ed, and Fran have reserved six seats in a row at the theater, starting at an aisle seat. (Refer to Example 8.)
In how many ways can they arrange themselves if the men and women are to alternate with either a man or a woman on the aisle? Arne, Chuck, and Ed are men, and the others are women. (Hint: First answer the following six questions in order.)
(a) How many choices of people are there for the aisle seat?
(b) Now, how many are there for the second seat? (This person must not be of the same gender as the person on the aisle.)
(c) Now, how many choices are there for the third seat?
(d) Now, how many for the fourth seat?
(e) Now, how many for the fifth seat?
(f) Now, how many for the sixth seat?
Now multiply your six answers above.
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- A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in the front and 3 in the back a. How many arrangements are possible with no restrictions? b. How many arrangements are possible if the parents must sit in the front? C. How many arrangements are possible if the parents must be next to each other?arrow_forwardPlacing people in line In how many arrangements can 5 women and 5 men be placed in a line if the women and men alternate?arrow_forwardIn Example 10, the team must consist of six boys and six girls. How many different 12-member teams are possible?arrow_forward
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