Group of 5 girls and 12 boys sitting in 17 seats
Source: Vietnamese National Mathematical Olympiad 2012-P5
February 8, 2012
combinatorics proposedcombinatorics
Problem Statement
For a group of 5 girls, denoted as and boys. There are chairs arranged in a row. The students have been grouped to sit in the seats such that the following conditions are simultaneously met:
(a) Each chair has a proper seat.
(b) The order, from left to right, of the girls seating is
(c) Between and there are at least three boys.
(d) Between and there are at least one boy and most four boys.
How many such arrangements are possible?