a. A dinner club has 30 members. At a particular dinner, every club member gets to order exactly 3 different items. How many items must be available so that every member of the club can have a different dinner – i.e. no two dinners have exactly the same three items? [don’t try manually, use excel builtin] b. Stacy has the option of selecting three books to read for a humanities course. The suggested book list consists of 10 biographies and five current events books. She decides to select the three books at random. Find the probability that all three books selected will be current events books.
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.
a. A dinner club has 30 members. At a particular dinner, every club member gets to order exactly
3 different items. How many items must be available so that every member of the club can have
a different dinner – i.e. no two dinners have exactly the same three items? [don’t try manually,
use excel builtin]
b. Stacy has the option of selecting three books to read for a humanities course. The suggested
book list consists of 10 biographies and five current
books at random. Find the probability that all three books selected will be current events books.
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