# Quiz #10 Answers July 23, 2014 Math 141

```Quiz #10a
July 23, 2014
Math 141
1. An exam contains five multiple choice questions each with 6 answers and 2 true/false questions. How many different ways can a student answer the exam if they are allowed to leave
questions blank?
7 ∗ 7 ∗ 7 ∗ 7 ∗ 7 ∗ 3 ∗ 3 = 75 ∗ 32
2. In how many ways can 7 boys and 3 girls be seated in a row if a girl must sit at both ends of
the row?
3∗8∗7∗6∗5∗4∗3∗2∗1∗2
3. How many three-letter identification codes can be constructed from the first 10 letters of the
alphabet if the first letter must be a B, a C, or a D and no letters may occur more than once.
3∗9∗8
4. A group of friends has 10 boys and 7 girls. They want to take a picture that have 5 kids
in a row with the additional condition that the boys and girls have to alternate. How many
different pictures are possible?
alternating seats will be bgbgb or gbgbg
10 ∗ 7 ∗ 9 ∗ 6 ∗ 8 + 7 ∗ 10 ∗ 6 ∗ 9 ∗ 5
5. A club consists of 15 freshmen, 20 sophomores, 10 juniors, and 25 seniors. Seven members of
the club are selected to win a prize of \$100. How many ways can this group be selected if it
will contain exactly one freshman, exactly one sophomore and exactly two juniors.
C(15, 1)C(20, 1)C(10, 2)C(25, 3)
```