1.8: Trophy arrangements and team selection

0606/13/M/J/19 — Question 9 · 11 marks

(a)(i)
Jack has won 7 trophies for sport and wants to arrange them on a shelf. He has 2 trophies for cricket, 4 trophies for football and 1 trophy for swimming. Find the number of different arrangements if there are no restrictions.
[1]
(a)(ii)
Jack has won 7 trophies for sport and wants to arrange them on a shelf. He has 2 trophies for cricket, 4 trophies for football and 1 trophy for swimming. Find the number of different arrangements if the football trophies are to be kept together.
[3]
(a)(iii)
Jack has won 7 trophies for sport and wants to arrange them on a shelf. He has 2 trophies for cricket, 4 trophies for football and 1 trophy for swimming. Find the number of different arrangements if the football trophies are to be kept together and the cricket trophies are to be kept together.
[3]
(b)(i)
A team of 8 players is to be chosen from 6 girls and 8 boys. Find the number of different ways the team may be chosen if there are no restrictions.
[1]
(b)(ii)
A team of 8 players is to be chosen from 6 girls and 8 boys. Find the number of different ways the team may be chosen if all the girls are in the team.
[1]
(b)(iii)
A team of 8 players is to be chosen from 6 girls and 8 boys. Find the number of different ways the team may be chosen if at least 1 girl is in the team.
[2]