1) A salad consisting of 5 types of vegetables and/or cheeses must be made from 7 types of cheeses and 6 different types of nuts.
(a) How many salads can be made with the condition that at least one type of vegetable should be included?
I know the answer to this one is 1281, but I am struggling to get to it. I thought the answer would be 7C1 x 13C4 but that gives me 5005.
(b) How many salads can be made if at least 2 types of vegetables and at least 2 types of cheeses must be included?
Again, the answer I know to be 945, but all my attempts have been in vain.
2) You have 2 apples, 3 oranges, 5 walnuts, and 3 guavas. You have to make a salad of 4 fruits - how many ways can this be done?
3) There are 10 cars, 4 of which are red, 3 of which are blue, and 3 of which are green - how many ways can you put 3 cars in a showroom so that there are at least 2 different colors?