FALL 2015
MATH 141 - ASSIGNMENT (6.1-6.4)
DUE: 10/19/15
Name
All steps must be written clearly and neatly to get full credit. If you use your calculator for anything beyond an arithmetic calculation, please indicate how at the appropriate step.
1. (10pts) In a study of factors that influence brand switching by 18- to 24-year-old female college students, the following factors were identified as being significant as judged by the responses of the 439 participants in the survey:
1: Better price 2: Friend’s recommendation 3: Seeing others use it
4: Interesting packaging 5: Buzz - people talking about the brand
6: An advertisement 7: Press stories 8: Entertainer/sports celebrity endorsement
The results of the survey follow:
Factor 1 2 3 4 5 6 7 8
Respondents (%) 68.8 60.4 22.8 20.8 16.8 16.8 14.9 6.9
Let A denote the set of factors that had a response greater than 20%, let B denote the set of factors that had a response between 15% and 25%, and let C denote the set of factors that had a response less than 25%. Find
(i) n ( A ) , n ( B ) , n ( C )
(ii) n ( A ∩ B ) by using the addition rule in the appropriate way
(iii) n ( A c ∩ C )
(iv) n [( A ∪ B ) ∩ C ]
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2 ASSIGNMENT (6.1-6.4)
2. (20pts) Jack and Jill and 5 of their friends go to the movies. They all sit next to each other in the same row. How many ways can this be done if
(i) There are no restrictions?
(ii) Jill must sit in the middle?
(iii) Jill sits on one end of the row, and Jack sits on the other end of the row?
(iv) Jack, Jill, or John sits in the middle seat?
(v) Jack, Jill, and John sit together in the middle three seats?
(vi) Jack and Jill must sit next to each other?
(vii) Jill must not sit next to Jack?

ASSIGNMENT (6.1-6.4)
3. (5pts) A student taking an examination is required to answer exactly 10 out of 15 questions.
(i) In how many ways can the 10 questions be selected?
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(ii) In how many ways can the 10 questions be selected if exactly 2 of the first 3 questions must be answered?
4. (5pts) How many distinct ten-digit numbers can be made using the digits
1 , 2 , 2 , 3 , 3 , 3 , 4 , 5 , 6 , 6?