# Quiz #10 Answers July 23, 2014 Math 141

```Quiz #10b
July 23, 2014
Math 141
1. An exam contains six multiple choice questions each with 3 answers and 2 true/false questions.
How many different ways can a student answer the exam if they are allowed to leave questions
blank?
4 ∗ 4 ∗ 4 ∗ 4 ∗ 4 ∗ 4 ∗ 3 ∗ 3 = 46 ∗ 32
2. In how many ways can 5 boys and 4 girls be seated in a row if a girl must sit at both ends of
the row?
4∗7∗6∗5∗4∗3∗2∗1∗3
3. How many three-letter identification codes can be constructed from the first 15 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 ∗ 14 ∗ 13
4. A group of friends has 8 boys and 5 girls. They want to take some pictures that have 3 boys
and 2 girls in a row in the picture with the additional condition that the boys and girls have
to alternate. How many different pictures are possible?
alternate means bgbgb or gbgbg
8∗5∗7∗4∗6+5∗8∗4∗7∗3
5. A club consists of 10 freshmen, 6 sophomores, 8 juniors, and 5 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(10, 1)C(6, 1)C(8, 2)C(5, 3)
```