
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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Chapter 7 Solutions
USING+UNDERSTANDING MATH.(LL)-W/MYMATH.
- Prove that (1) Σσς (α) μ(η/α) = n d/n (ii) Σσς(d) = η Σσο(α)/d d❘n d❘n (iii) σ (d) σ (n/d) = Σ d³oo(d) σo(n/d). d|n dnarrow_forwardII Consider the following data matrix X: X1 X2 0.5 0.4 0.2 0.5 0.5 0.5 10.3 10 10.1 10.4 10.1 10.5 What will the resulting clusters be when using the k-Means method with k = 2. In your own words, explain why this result is indeed expected, i.e. why this clustering minimises the ESS map.arrow_forwardX Acellus | Student admin192c.acellus.com go 0:0 Hannah wants to have concrete stairs for her backdoor. How much concrete will be needed to build the stairs? 20 cm 70 cm 30 cm 15 cm 10 cm 45 cm cm 70 cm GIF 自 لاarrow_forward
- why the answer is 3 and 10?arrow_forward1 Hannah wants to have concrete stairs for her backdoor. How much concrete will be needed to build the stairs? 70 cm 30 cm 15 cm 10 cm 10 cm 20 cm 45 cm cm³ GIF GIF/ 2 3 4 qwe asdf 5 6 自 yu ty u 8 ghjk 9 P Z X C cv b vbnm ×arrow_forwardPS 9 Two films are shown on screen A and screen B at a cinema each evening. The numbers of people viewing the films on 12 consecutive evenings are shown in the back-to-back stem-and-leaf diagram. Screen A (12) Screen B (12) 8 037 34 7 6 4 0 534 74 1645678 92 71689 Key: 116|4 represents 61 viewers for A and 64 viewers for B A second stem-and-leaf diagram (with rows of the same width as the previous diagram) is drawn showing the total number of people viewing films at the cinema on each of these 12 evenings. Find the least and greatest possible number of rows that this second diagram could have. TIP On the evening when 30 people viewed films on screen A, there could have been as few as 37 or as many as 79 people viewing films on screen B.arrow_forward
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