Concept explainers
Counting Methods. Answer the following questions us-
ing the appropriate counting technique. which may be either
arrangements with repetition. permutations. Or combinations.
Be sure to explain why this counting technique applies to the
problem.
23. HOW many different nine-digit ZIP codes can be formed?
24. How many different six-character can formed
from the lowercase letters of the ?
25. HOW many different six-character passwords can formed
from the lowercase letters of the alphabet if repetition is not
allowed?
26. A city council with eight members must elect a
executive committee consisting of a mayor, secretary, and
treasurer. How many executive committees are possible?
27. How many ways can the eight performances at a piano recital
be ordered?
28. A city council with ten members must appoint a four-person
subcommittee. How many subcommittees are possible?
29. Suppose you have 15 CDs from which you 6 CDs to
put in the CD player in your car. If you are not particular
about the order, how many O-CD sets are possible?
30.HOW many 6-person can be formed from a & player
volleyball assuming every player can be assign to
any position?
31. How many different birth orders with respect to gender
possible in a family with five children? (For example.
and BGBGG are different orders.)
32. HOW many different 5-cards can be dealt from a 52-card
deck?
33. How many license plates can be made of the form XX—YYYY,
where X is a letter Of the and Y is a numeral 0—9?
34. How many different groups of balls can drawn from
a barrel containing balls numbered 1—36?
35. How many different telephone numbers of the form aaa-bbb-
cccc formed if the area code cannot contain 0 and
the prefix bbb cannot contain 9?
36. HOW many anagrams (rearrangements) Of the letters
ILOVEMATH can nuke?
37. How many different three-letter “words”- can formed from
the ACGT?
38. The debate club has 18 members, but only 4 can compete
at the next meet. How many 4-Frson teams are possible?
39. A recording engineer wants to make a CD With 12 songs. In
how many different ways can the CD nude?
40. A shelter is giving away 15 but you have
room for only 4 of them. How many different families
could you have?
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Check out a sample textbook solutionChapter 7 Solutions
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
- a In solving a problem involving picking r objects from n objects, how do you know whether to use permutations or combinations? b Would you use combinations or permutations in counting the following: i The number of five-card hands from a 52-card deck. ii The number of ways in which first, second, and third prizes can be awarded in a ten-person race.arrow_forwardChoosing Officers From a pool of 12 candidates, the offices of president, vice-president, secretary, and treasurer need to be filled. In how many different ways can the offices be filled?arrow_forward
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