2.4: Television arrangements and group selection
(a)(i)[1]
Eleven different television sets are to be displayed in a line in a large shop. Find the number of different ways the televisions can be arranged.
(a)(ii)[2]
Of these television sets, 6 are made by company A and 5 are made by company B. Find the number of different ways the televisions can be arranged so that no two sets made by company A are next to each other.
(b)(i)[2]
A group of people is to be selected from 5 women and 3 men. Calculate the number of different groups of 4 people that have exactly 3 women.
(b)(ii)[2]
A group of people is to be selected from 5 women and 3 men. Calculate the number of different groups of at most 4 people where the number of women is the same as the number of men.