Determine if each is a permutation or a combination and then evaluate. 32. How many groups of three letters can be formed from the first five letters of the alphabet, if no letter can be repeated? 33. In how many ways can four students be seated in a row of four seats? 34. In how many ways can five people line up at a checkout counter in a supermarket?
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.
Determine if each is a permutation or a combination and then evaluate.
32. How many groups of three letters can be formed from the first five letters of the alphabet, if no letter can be repeated?
33. In how many ways can four students be seated in a row of four seats?
34. In how many ways can five people line up at a checkout counter in a supermarket?
35. How many different batting orders can be formed for a nine-member baseball team?
36. In how many ways can the names of six candidates for political office be listed on a ballot?
37. In how many ways can a member of a hiring committee select 3 of 12 job applicants for further consideration?
38. In how many ways can an investor select four mutual funds for his investment portfolio from a recommended list of
eight mutual funds?
45. In how many ways can a supermarket chain select 4 of 12 possible sites for the construction of a new supermarket?
46. A student is given a reading list of ten books from which he must select two for an outside reading requirement. In
how many ways can he make his selections?
47. In how many ways can a quality-control engineer select a sample of 3 microprocessors for testing from a batch of 100
microprocessors?
50. Seven people arrive at the ticket counter of a movie theater. In how many ways can they line up to buy their tickets?
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