MAT 112, Finite Mathematics - Worksheet #16
Counting and Probability
Name:_____________________
1. Consider a club with 12 members. Suppose 5 are boys and 7 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 we require one of the officers to be a boy and the other a girl?
c). If a group of 5 members are selected for a project, how many different groups are
possible?
d). If a group of 5 members are selected for a project, how many different groups are
possible which include 3 boys and 2 girls?
e). If a group of 5 members are selected for a project, how many different groups are
possible which include only girls?
f). If a group of 5 members are selected for a project, how many different groups are
possible which include 4 or 5 girls?
g). If a group of 5 members are selected for a project, how many different groups are
possible which include exactly 2 girls or exactly 2 boys?
2. Suppose a 5-card hand is dealt from a deck of 52 playing cards.
a). How many ways can a 5-card hand result in 5 spades?
b). How many ways can a 5-card hand result in exactly 3 spades?
c). How many ways can a 5-card hand result in 5 non-face cards?
d). How many ways can a 5-card hand result in exactly 2 face cards?
3. Suppose a 7-card hand is dealt from a deck of 52 playing cards.
a). How many 7-card hands are possible?
b). How many 7-card hands contain exactly 5 spades?
c). How many 7-card hands include 5 or more spades?
d). How many 7-card hands include no spades?
4. Suppose your jazz collection includes 4 Yellowjackets CDs, 6 Najee CDs,
and 5 Spyro Gyra CDs. For each question below, show your setup and make the
calculation.
a). If you’re asked to rank your 3 favorite CDs from this collection, how many outcomes
are possible?
b). If you’re asked to choose your favorite CD by each of the groups above (a total of
3 CDs), how many outcomes are possible?
c). Suppose you take 5 of these jazz CDs along in your car. How many collections of
5 CDs are possible?
d). Suppose you take 5 of the CDs along in your car. How many collections of 5 CDs
are possible if they include 2 Yellowjacket CDs and 3 Najee CDs.
e). Suppose you take 5 of the CDs along in your car. How many collections of 5 CDs
are possible which include exactly 3 Najee CDs.
f). How many collections of 5 CDs are possible which include no Yellowjackets CDs?