Question 462004: Can a kind tutor please tell me if I did these difficult homework problems correctly?
7. Of the 100 people who were given a new sleeping aid, 30 experienced a light headache, 18 experienced a reduced appetite, and 60 experienced neither side-effect. How many people experienced both a light headache and a reduced appetite?
60-48 - 12?
8. A quiz consists of 6 multiple-choice questions, each has three possible answers. In how many different ways can the quiz be answered if one answer is chosen for each question?
3^6= 729?
9. A code consists of two letters chosen from the English alphabet, followed by 4 digits. If the first letter must be a K or an M, the second letter can be any one of the 26 letters, how many different codes are possible?
2 x 26= 52 x 10^4= 52,000?
10.In how many ways can two math books and three English books be arranged in a row if the two math books must be placed next to each other?
4!?
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website! Can a kind tutor please tell me if I did these difficult homework problems correctly?
7. Of the 100 people who were given a new sleeping aid,
30 experienced a light headache, 18 experienced a reduced
appetite, and 60 experienced neither side-effect. How many
people experienced both a light headache and a reduced appetite?
60-48 - 12?
No that's wrong
Let A = set of those with a light headache
Let B = set of those with a reduced appetite
N(A OR B) = N(A) + N(B) - N(A AND B)
Since 60 experienced neither, 100-60 or 40 experienced
one OR the other.
So N(A OR B) = 40
We are given N(A) = 30 and N(B) = 18
We want to find N(A AND B). Let that = x:
N(A OR B) = N(A) + N(B) - N(A AND B)
40 = 30 + 18 - x
40 = 48 - x
x = 8
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8. A quiz consists of 6 multiple-choice questions,
each has three possible answers. In how many different
ways can the quiz be answered if one answer is chosen
for each question?
3^6= 729?
That's correct.
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9. A code consists of two letters chosen from the English
alphabet, followed by 4 digits. If the first letter must
be a K or an M, the second letter can be any one of the
26 letters, how many different codes are possible?
2 x 26= 52 x 10^4= 52,000?
You shouldn't put the intermediate step of 52 inside
the equation. You should have
2 x 26 x 10^4 =
and then the answer is 520,000, not what you have, You
need another 0.
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10.In how many ways can two math books and three
English books be arranged in a row if the two math
books must be placed next to each other?
4!?
No, that's wrong.
We have one of 4 configurations:
MMEEE, EMMEE, EEMME, EEEMM
That's 4 choices for the configurations
For each of those configurations we can arrange the
2 math books 2! ways. That's 4 x 2! ways to choose
the configuration and the math books.
For each of those 4 x 2! ways, there are 3! ways
to arrange the 3 English books.
So the answer is 4 x 2! x 3! = 4 x 2 x 6 = 48 ways.
Edwin
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