MAT 112, Finite Mathematics - Worksheet #15 Name:______
1. Given that , , , and , determine the number of elements in each of the subsets identified below.
a). has ______elements
b). has ______elements
c). has ______elements
d). has ______elements
2. A group of 100 people touring Europe includes 38 people who speak French, 45 who speak German, and 11 who speak both languages. How many people in the group speak neither French nor German?
3. Consider a club with 9 members. Suppose 5 are boys and 4 are girls.
a). If the club elects a president and vice-president, how many different outcomes are
possible?
b). If the club elects a president and vice-president, how many different outcomes are
possible if one of these officers is a boy and the other is a girl?
c). If the members are lined up in two rows for a photograph, with the boys in the
back row and the girls in front, how many such arrangements are possible?
4. Suppose you place your 7 George Straight CDs on a shelf along with your daughter’s
5 Britney Spears CDs.
a). How many ways (side-by-side arrangements) can the CDs be arranged on the
shelf?
b). If you keep the Straight CDs on the left side of the shelf and the Spears CDs on
the right, how many ways can the CDs be arranged?
c). Suppose there are 9 songs on a CD and you play them in random order, playing
each song just once. How many different orderings of the songs are possible?
d). Suppose there are 9 songs on a CD and you play them in random order, allowing
the same song to be repeated. How many different arrangements are possible if
you listen to just 5 songs?
5. Suppose a state produces license plates with two capital letters followed by four digits. The letters and digits may be repeated. For example, BB 1438, and WP 6833 are possible license plates.
a). How many different license plates can be produced?
b). How many of these license plates have an “A” as the first letter?
c). Determine the number of these license plates such that the first letter or the
second letter is an “A”?
6. Given 12 items, to count the number of ways to choose and arrange 6 of the items,
we may use the multiplication rule or use permutations. Compare the following two calculations:
a). The product: ( 12 )( 11 )( 10 )( 9 )(8)(7) = ______?
b). The number of permutations: ______?