advertisement

Quiz #10b Answers 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)