Chapter 7.E, Problem 24E

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?