combinations and binomial theorem

[bsrrjr]

Hi. I tried these questions however i am unable to do them:embarass:

 

Question1.

There are 52 white keys on a piano.The lowest key is A. The keys are designated A,B,C,D,E,F and G in succession, and the sequence of letters repeats, ending with a C for the highest key.

a) If five notes are played simultaneously, in how many ways could the notes all be i) As? ii) Gs

iii) the same letter? iv) different letters?

b) If the five keys are played in order, how would your answers in part a) change?

 

 

Question2. A basketball team consists of five players-one centre, two forwards, and two guards. The senior squad has two centres, six forwards, and four guards.

a) How many ways can the coach pick the two starting guards for a game?

b) How many different starting lineups are possible if all team members play their specified positions?

c) How many different starting lineups include Dana, the team's 185cm center?

d) Some coaches designaate the forwards as power forward and small forward. If all six forwards are adept in either position, how would this designation affect the number of possible starting lineups?

e) As the league final approaches, the centre Dana, forward Ashlee, and guard Hollie, are all down with a nasty flu. Fortunately, the five healthy forwards can also play the guard position. If the coach can assign these players as either forwards or guards, will the number of possible starting lineups be close to the number in part b)? Support your answer mathematically

f) Isthe same result acheived if the forwards play their regular positions but the guards can play as either forwards or guards? Explain your answer