MATH 166 Spring 2016
2.2
c
Wen
Liu
2.2 Combinations
Definition: A combination of r distinct objects taken from a set of size n is a selection of r of the
objects (without concern for order).
Number of Combinations of r Objects taken from a Set of Size n: The number of combinations of r distinct objects taken from a set of size n, denoted by C(n, r), is given by
C(n, r) =
n!
r!(n − r)!
Technology Corner: To compute C(n, r): enter n, press MATH , arrow over to the PRB menu,
choose 3: nCr, and enter r
Examples:
1. JCL Computers has five vacancies in its executive trainee program. In how many ways can the
company select five trainees from a group of 15 female and 15 male applicants if the vacancies
(a) Can be filled by any combination of men and women?
(b) Must be filled by two men and three women?
2. Six prizes are to be given to six different people in a group of eleven. In how many ways can a
first prize, a second prize, a third prize and three fourth prizes be given?
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MATH 166 Spring 2016
2.2
c
Wen
Liu
3. A box contains 12 red marbles, 6 green marbles, and 8 black marbles. For questions (a)-(c), a
sample of 11 marbles is to be picked from the box.
(a) How many samples contain at least 1 red marble?
(b) How many samples contain exactly 4 red marbles and exactly 3 black marbles?
(c) How many samples contain exactly 7 red marbles or exactly 6 green marbles?
(d) A sample of 4 is to be picked from the box. In how many ways can a sample be selected
so that exactly 3 of the marbles are the same color?
(e) A sample of 8 is to be picked from the box. In how many ways can a sample be selected
so that at least 5 of the marbles are red?
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