Worksheet – Combinations
Mr. Chvatal
A combination of n objects taken r at a time is denoted by n Cr . In combinations, order
does not matter.
Playing cards
Examples
1.
Given a standard 52-card deck, how many different five-card hands are possible?
2.
In how many hands are all five cards the same color?
3.
In how many hands are all five cards the same suit?
4.
Four face cards and one that is not a face card?
5.
Three queens and two that are not queens?
6.
Full house (three of one kind, two of a different kind)?
7.
Royal flush (10, J, Q, K and ace of the same suit)?
8.
At least one heart?
9.
At least one ace?
10.
At most two spades?
Jelly beans
A bag contains 14 red jelly beans, 7 green, 9 yellow, and 6 blue. You will note that these
problems require exactly the same approach as problems with playing cards.
11.
How many combinations of two green, four yellow, and three red jelly beans are
possible out of a selection of nine? What are the odds of drawing this
combination?
12.
Ten jelly beans are drawn. How many combinations are possible in which exactly
four are not red? What are the odds of drawing this combination, as a percentage?
Miscellaneous
13.
Ten students volunteer to help raise money at the senior class car wash. One
student will be assigned to handle the money, three to hold up signs, four to wash
and two to towel dry. How many different combinations of assignments can be
made?
14.
A committee of three people is to be chosen from seven students: Alan, Bill,
Charlotte, Denise, Ernie, Frank and Georgia. What is the probability (in percent)
that:
a) Frank is chosen.
b) Alan and Denise are chosen.
c) Bill is chosen but not Georgia.
d) Ernie or Charlotte is chosen.