Probability question on Coupons

Question

Suppose there are M different coupons. All coupons are equally likely to come.
You collected your Nth coupon.

What is the probability that

a) Your current coupon is different than what you had in your hand just before it?
    (different than all other coupons you have)

b) You have all distinct coupons till this time?

c) Expected number of different types of coupon you have currently.

Comments

a) $\frac{M-1}{M}$

b) $\frac{M*(M-1)*(M-2)*....(M-N+1)}{M^{N}}$

c) I guess

E(X) = $0*\frac{\binom{M}{1}*\binom{N}{0}}{M^{N}}$ + $2*\frac{\binom{M}{2}*\binom{N+1}{1}}{M^{N}}$ +..... + $N*\frac{\binom{M}{N}*\binom{N+N-1}{N-1}}{M^{N}}$

Answer 1

Sir,  I have made an attempt.I don,t whether it is correct or not