Table of Contents
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1. Practice
- 1.1. # of binary sequences w/non conesecutive four 1’s
- 1.2. How many triangles are there with vertices from the points shown below? This does not include triangles with the 3 points on the same line.
- 1.3. There are 50 students enrolled in the second year of a business degree program. During this semester, the students have to take some elective courses. 18 students decide to take an elective in psychology, 27 students decide to take an elective in geography, and 10 students decide to take an elective in both psychology and geography. What is the probability that a student takes an elective in psychology or geography?
1. Practice
1.1. # of binary sequences w/non conesecutive four 1’s
e.g
101010100
010101010
_OOOOOO-
7 spaces:
S1, S2, S3, S4, S5, S6, S7
S1S2S3S4
s1s2s3s4 = s4s3s2s1
Order Doesnt matter!
(7*6*5*4)/4! = 35 sequences w/o four consecutive 1’s!
or using formula…
combination n = 7 r = 4
7!/4! = 35
1.2. How many triangles are there with vertices from the points shown below? This does not include triangles with the 3 points on the same line.
- Label each dot with letters
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write samples
- ABF, ABG, BAG, CAF
- ABF = BAF, order does not matter
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Slot Method
- two possibilites for the first two letters and the last one from the other line.
- ABF (5*4/2!)*6!=60
- FGB (6*5/2!)*4=60
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General Addition becuase we can start on the left or bottom
- 60 + 60 = 120
1.3. There are 50 students enrolled in the second year of a business degree program. During this semester, the students have to take some elective courses. 18 students decide to take an elective in psychology, 27 students decide to take an elective in geography, and 10 students decide to take an elective in both psychology and geography. What is the probability that a student takes an elective in psychology or geography?
P(P) = 18/50
p(g) = 27/50
P(PnG) = 10/50
P(PuG) = P(P) + P(G) - P(PnG)