MTH 157 Mon, .July 23, 2018 PROBABILITY TEST 4 COUNTING TEOedaesao You must use
ID: 2908126 • Letter: M
Question
MTH 157 Mon, .July 23, 2018 PROBABILITY TEST 4 COUNTING TEOedaesao You must use pencil, erase clearly, be neat and onderty. Yeu must show your steps. What numbers are you using and how are you using them to get your answers. Dem just give m. on.???. Iwill count it totally wrog Allu ers must b. spp ed by your work. Your work must be orgonized so that I can understand how you get from one step to another step. There are blanks on the right side of the test pages, Use them to place you final answers upon. 1.There are 26 letters in our alphabet. The vowels are A, E, 1, O. U. you cannot use the vowels. The digits to be used are: 0, 1, 2, 3, 4, 5,6. 7. 8 9. You do not need to multiply the mumbers together. Just use a det for times. a. How many different license plates can be made with three of the allowed letters and three digits (omit O and 7)? b. How many different license plates can be made with three of the letters (do not repeat any of the allowed letters) and three digits? e. How many different license plates con be made using 6 digits all of which must be odd? d. How many different license plates can be made with three of the allowed letters (no repetition is allowed with the letters) and three digits (the second digit must be zero)? The office has 3 women and 4 men. All of these employees have equal credentials. From these 7 people, the boss will choose two directors. In how many ways can the boss choose two directors? 2.Explanation / Answer
a.
choose any letter for each of those positions exclude the vowels ( 5 letters)
21*21*21=9261
choose any digit for each of the other positions omitted 0 and 7 ( 2digits)
8*8*8= 512
Total number of license plates
9261*512= 4,741,632
b.
choose any letter for each of those positions exclude the vowels ( 5 letters) with no repetition
21*20*19 = 7980
choose any digit for each of the other positions
10*10*10 = 1000
Total number of license plates
7980*1000 =7,980,000
c.choose odd digit for 10 digit number is
5^6= 15625
d.
choose any letter for each of those positions exclude the vowels ( 5 letters) with no repetition
21*20*19 = 7980
Choose digit
10*1*10=100
TOtal
7980*100 = 798000
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