(a) A student is asked to answer 11 out of 13 questions on a exam. In how many
ways can she select the questions to be answered?(Order is not important).
C(13,11) = C(13,13-11) = C(13,2) = = = 78
(b) In how many ways can a chairperson and a vice chairperson be selected from a
committee of 15 senators?
P(15,2) = 15*14 = 210
(c)How many permutations are there of the following word?
COMBINATORICS
If the 2 C's, the 2 I's, and the 2 O's were distinguishable, the answer would be
P(13,13) = 13! since it is a 13-letter word. However since they are not
distinguishable, we must divide by the factorial of each:
= = 778377600
(d) Tarot cards are used for telling fortunes, and in a reading, the arrangement
of the cards is as important as the cards themselves. How many different
readings are possible if four cards are selected from a set of eight Tarot
cards?
P(8,4) = 8*7*6*5 = 1680
(E)A state's license plate consist of four letters followed by three numerals,
and 246 letter arrangements are not allowed. How many plates can the state
issue?
The number of possible letter arrangement, allowed or not, are
26*26*26*26 = 264 = 11881376
[Notice that permutations do not work because we can use each letter more than
once.]
From that we subtract the 246 arrangements which are not allowed.
That's 11881376-246 = 11881130
The number of digit arrangements is 10*10*10 = 103.
[Again permutations do not work because we can use the same digits more
than once.
So we multiply them tobether and get 11881376*1000 = 11881376000.
Edwin