Browse · MATH
Printjmc
counting and probability intermediate
Problem
The Smith family has 4 sons and 3 daughters. In how many ways can they be seated in a row of 7 chairs such that all 3 girls sit next to each other?
Solution
We want to deal with the restriction first.
Without worrying about which specific boys and girls go in which seats, in how many ways can the girls sit together?
There are 5 basic configurations of boys and girls: where is a boy and is a girl. Then, within each configuration, there are ways in which we can assign the 4 sons to seats, and ways in which we can assign the 3 daughters to seats.
Therefore the number of possible seatings is .
Without worrying about which specific boys and girls go in which seats, in how many ways can the girls sit together?
There are 5 basic configurations of boys and girls: where is a boy and is a girl. Then, within each configuration, there are ways in which we can assign the 4 sons to seats, and ways in which we can assign the 3 daughters to seats.
Therefore the number of possible seatings is .
Final answer
720