Kabaddi is a popular sport in South Asia. The basic rules of Kabaddi are

simple: two teams of seven players each face off in a large square arena for two halves of

twenty minutes each. Players from each team take turns running across the center line to

the other team's half of the court ( called "raiding"), tagging members of the other team

(4 people defending), and running back. The more opposing team members they tag, the

more points they score (+1 point for each player he tags), but if the opposing team can

physically prevent them from crossing back to their side of the court, they score no points.

During the sports week, a kabaddi match is going to be scheduled between the students of

Section B and D. Section B has 37 students while Section D has 38 students

(a) In how many ways can a team from each of the class be selected. (3)

(b) During the match there is 15% chance of a player being injured in which case a replacement has to be sent in. How many students should be put on bench (including the 7 players) for each team so that there is 80% probability of having enough replacement

players for the entire match. (3)

(c) During a raid, there is 10% chance of tagging an opposing team member and successfully returning back, 40% chance of being caught by that player and 50% chance of

returning back without tagging. What is probability of scoring 1 point for the raid.

What is the probability of scoring 4 points for the raid.

Assume that the raider deals with each defender independently