Permutations and combinations
I have three questions, the first two are similar.
1)Four boxes each containing a large number of identical balls, those in one box are red, those in the second box are blue, those in the third box are yellow, and those in the remaining box are green. In how many ways can a set of five balls be chosen if:
a) there is no restriction
b) at least one ball is red?
For a) i think the answer should be but the answer is 56. For b) i think it should be but the answer is 35.
2)In how many ways can four tins of fruit be chosen from a supermarket offering ten varieties if at least two of the tins are of the same variety?
There are at least two cans that are the same, so we have two same, three same, and all same. I did for two same, for three same, and 10 for all same. Total would be 820, but the answer is supposed to be 505.
3)A certain test consists of seven questions, to each of which a candidate must give one of three possible answers. According to the answer that he chooses, the candidate must score 1,2, or 3 marks for each of the seven questions. In how many ways can a candidate score exactly 18 marks in the test?
I don't know how to begin this question.
Thanks for any help!