Salads and Cars
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?
I think that you need to supply more information about #1. Surely there are some details missing. How is the salad to be made? How many vegetables are to be used? Is it from zero to five? Same question about the cheeses and nuts.
The given answer of 1281 does not give any guidance.
It seems that you need to review this posting and correct it. Please post the whole question as given.