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Count nonempty subsets and a selection with tomatoes fixed

The salad bar at a restaurant has 6 separate bowls containing lettuce, tomatoes, cucumber, radishes, spring onions and beetroot respectively. John decides to visit the salad bar and make a selection. At each bowl, he can choose to take some of the contents or not.

(i) Assuming that John takes some of the contents from at least one bowl, find how many different selections he can make.

(ii) John decides he is going to have 4 salad items, and one of them will be tomatoes. How many different selections can he make?

[1999/I/18(b)]

CJC · Discussion · Question 11

Treat each bowl as a yes/no choice.

Read the worked solution