Extremely difficult question: "A rugby union squad has 30 players...."

Rakesh1234

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A rugby union squad has 30 players.

(a) How many ways are there or forming a team of 15 players from the squad?

(b) Half of the squad are forward players, while the other half are backs. In a team there are 8forwards and 7 backs. How many ways are there of forming the team from the squad so that noforward player plays in the backs, and vice-versa?

(c) The fly-half (back) is a position where only an expert can play. An expert fly-half can play inno other position. There are 2 fly-halves in the squad and the rest of the squad is equally splitbetween forwards and backs. How many ways are there of forming a team from the squad?

(d) Now suppose all positions 1-15 require expert players and a squad must have at least one of eachof these players. How many ways are there of forming a squad?
 
Such a lovely problem. Please demonstrate your efforts.
 
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