Phoebe surveyed teens and adults to find the average number of hours of sleep they get during the week. Her results are shown be
2 answers:
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Answer:
(a)
(b)
(c)
(d)
Step-by-step explanation:
Given
--- at least
Solving (a): 28 combinations
From the question, we understand that; a combination of 28 is to be selected. Because the order is not important, we make use of combination.
Also, because repetition is allowed; different balloons of the same kind can be selected over and over again.
So:
Solving (b): At most 12 red balloons
First, we calculate the ways of selecting at least 13 balloons
Out of the 28 balloons, there are 15 balloons remaining (i.e. 28 - 13)
So:
Selection of at least 13 =
Ways of selecting at most 12 =
--- Complement rule
Solving (c): At most 8 blue balloons
First, we calculate the ways of selecting at least 9 balloons
Out of the 28 balloons, there are 19 balloons remaining (i.e. 28 - 9)
So:
Selection of at least 9 =
Ways of selecting at most 8 =
--- Complement rule
Solving (d): 12 red and 8 blue balloons
First, we calculate the ways for selecting 13 red balloons and 9 blue balloons
Out of the 28 balloons, there are 6 balloons remaining (i.e. 28 - 13 - 9)
So:
Selection =
Using inclusion/exclusion rule of two sets: