MATH 166 Spring 2016
c
Wen
Liu
2.3
2.3 Probability Applications of Counting Principles
Distinguishable Permutations: A set of size n is divided into k groups of sizes n1 , n2 , . . . , nk ,
with all elements in each group being identical. Then the number of distinguishable permutations is
n!
n1 !n2 ! · · · nk !
where n1 + n2 + · · · + nk = n.
Recall: From section 1.4, the probability of an event E is given by
P (E) =
n(E)
n(S)
where n(E) is the number of outcomes in event E and n(S) is the number of outcomes in the uniform
sample space for this experiment.
Examples:
1. Four marbles are selected at random without replacement from a jar containing three white
marbles and five blue marbles. Find the probability of the given event-all of the marbles are
blue.
2. A 3-card hand is drawn from a standard deck of 52 playing cards. Find the probability that
the hand contains the given cards.
(a) no face cards (jack, queen, king).
(b) 3 cards of the same suit are drawn.
Page 1 of 2
MATH 166 Spring 2016
2.3
c
Wen
Liu
3. A box has 13 marbles, 6 of which are white and 7 of which are red. A sample of 7 marbles is
selected randomly from the box without replacement.
(a) What is the probability that exactly 5 are white and 2 are red?
(b) What is the probability that at least 5 of the marbles are white?
4. A student studying for a vocabulary test knows the meanings of 12 words from a list of 22
words. If the test contains 10 words from the study list, what is the probability that at least 8
of the words on the test are words that the student knows?
Page 2 of 2