3 A para relay team of 4 swimmers needs to be chosen from a group of 7 swimmers.
- How many ways are there to choose 4 swimmers from 7?
There are no restrictions on how many men and how many women are in the team. The group of 7 swimmers consists of 5 men and 2 women.
- How many ways are there to choose a team with more men than women?
The physical impairment of each swimmer is given a score.
The scores for the swimmers are
\(\begin{array} { l l l l l l l } 3 & 4 & 4 & 6 & 7 & 8 & 9 \end{array}\)
The total score for the team must be 20 or less. - How many different valid teams are possible?
The order of the swimmers in the team is now taken into consideration.
- In total, how many different arrangements are there of valid teams?
- In how many of these valid teams are the scores of the swimmers in increasing order? For example, 3, 4, 4, 8 but not 4, 3, 4, 8 .