Exercise 5.1.3: Selecting lunch specials for the week. (b) Now suppose that out of the 10 dishes that the restaurant offers, only 3 of them are vegetarian. If Fiona must select a vegetarian option on Friday, how many ways are there for her to select her lunches? (c) Again, suppose that out of the 10 dishes that the restaurant offers, only 3 of them are vegetarian. If Fiona must go with a vegetarian option on both Monday and Friday, how many ways are there for her to select her lunches? (d) Now suppose that Fiona can select a vegetarian or a non-vegetarian lunch on any day of the week. However, in addition to selecting her main course, she must also selects between water or tea for her drink. How many ways are there for her to select her lunches?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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Exercise 5.1.3: Selecting lunch specials for the week.
(b)
Now suppose that out of the 10 dishes that the restaurant offers, only 3 of them are vegetarian. If Fiona must select a vegetarian option on Friday, how many ways are there for her to select her lunches?
(c)
Again, suppose that out of the 10 dishes that the restaurant offers, only 3 of them are vegetarian. If Fiona must go with a vegetarian option on both Monday and Friday, how many ways are there for her to select her lunches?
(d)
Now suppose that Fiona can select a vegetarian or a non-vegetarian lunch on any day of the week. However, in addition to selecting her main course, she must also selects between water or tea for her drink. How many ways are there for her to select her lunches?
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