advanced combinatorics急急急急急!!~

要答案+解釋
1.find the number of all 10-digit integers in which no two consecutive digits are the same.

2.how many positive numbers smaller than 10^n such that their digits are non-decreasing from left to rigjt(e.g. 233344589)?

3.what is the number of ways to color n objects with 3 colors if every color must be used at least once?

4.in a round-robin tournament every player plays every other play.Suppose we give each person 2 points for a win,0 for a loss and 1 point for a tie.If 5 people are in the tournament,find the sum of their scores after all the matches have been played.(Does this depend upon the outcome of the games?)

5.a 5-card habd is randomly drawn from a standard 52-card deck.What is the probability of getting"three of a kind"?

6.one day a teacher decides to play a little game with his 50 students in class."I bet there are two of you having the same birthday!What do you think?"Many students think that the teacher has little chance of winning.BO you agree?Moreover,find the probability that the teacher wins.(you may need to use computer or programmable calculator to get the answer)

7.(random walk)Suppose you are at position"0"initially(see figure).Every time you flip a fiar coin,you move one atep to your right when you get a "head",and one step to your left when you get a "tail".
a)find the probability that you are at position"2"after flipping the coin 6 times.
b)find the probability that you are at posotion"0"again after flipping the coin n times.