NOTE: IS STUDYING \"DISCRETE MATHEMATICS FOR COMPUTER SCIENCE\" ABOUT PERMUATION
ID: 3728968 • Letter: N
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NOTE: IS STUDYING "DISCRETE MATHEMATICS FOR COMPUTER SCIENCE" ABOUT PERMUATION AND COMBINATION, AND WANT TO SEE THE WORK OF THE ANSWERS
5/5 pts Question 3 An organization has 10 male and 7 female members. In how many ways can the organization elect a president, a vice president, and secretary for each of the situations below? a) The president must be female 1680 b) The president may be male or female, but the vice president must be female, and the secretary must be male 1050 c) The president and vice president must be of the same sex 1980 d) All three officers may not be of the same sex 3150Explanation / Answer
a) The president must be female
So president can be elected from 7 female members in 7 ways.
Then we left with 16 members from which we can elect a vice president in 16 ways. Now we left with 15 members from which we can elect a secretary in 15 ways.
So total ways = 7x16x15 = 1680
b)
As vice president must be female, we can elect vice president in 7 ways.
As secretary must be male, we can elect secretary in 10 ways.
No we left with 15 members out which we can elect president in 15 ways.
total ways = 7x10x15 = 1050
c)
As president and vice president must be of same sex, we can choose two male or two female.
which is 10x9 + 7x6 = 90 + 42 = 132
Now we left with 15 members from which we can elect secretary in 15 ways.
total ways = 132x15 = 1980
d)
All three officers may not be of same sex, so we can calculate total ways to select them and remove the ways of selecting all of them from same sex.
total ways of selection = 17x16x15 = 4080
total ways of selecting three of them from same sex is selecting all of them from male or selecting all of them from female. which is 10x9x8 + 7x6x5 = 720 + 210 = 930
ways of selection when all may not be same sex = 4080 - 930 = 3150
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