7. For each question below, identify whether the situation is a permutation, com

Question

7. For each question below, identify whether the situation is a permutation, combination, or the basic law of counting, then find a solution to the question. a. The United States Postal Service currently uses 5-digit codes in most areas. How many zip codes are possible if they use the digits 0 -9 and none of the digits repeat? b. Over the weekend, your family is going on vacation, and your spouse is letting you bring the Nerf war equipment as well as five of your Nerf shields. How many ways can you choose the five shields if you have 12 shields in all? The local Symphony is preparing for a charity recital. The orchestra conductor needs to choose three pieces of music from a contract collection of 20 pieces of music. How many ways can the orchestra conductor choose the pieces of music? c. d. How many 3-letter code words on a lock are possible if someone can choose from the same 10 letters in each slot and letters can repeat?

Explanation / Answer

7-a)

Here basic principal of counting will be used.

We have 10 different digits.

First digit of code can be selected in 10 ways, second in 9 ways, 3rd in 8 ways, 4th in 7 ways and 5th in 6 ways. So possible number of 5 digits code is

10*9*8*7*6 = 30240

(b)

Order of shields in selection is not important. So combination will be used.

Possible number of selections of 5 shields out of 12 is C(12,5) = 792

(c)

Order of shields in selection is not important. So combination will be used.

Possible number of selections of 3 music pieces out of 20 is C(20,3) = 1140

(d)

Here basic counting principle will be used.

Possible number of codes is 10*10*10 = 1000

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