College Algebra & Trigonometry, 2018a

7.4. GENERAL COMBINATORICS PROBLEMS 321
3) Suppose that a department contains 10 men and 15 women. How many
ways are there to form a committee with 6 members if it must have the same
number of men and women?
4) The English alphabet contains 21 consonants and 5 vowels. How many
strings of 6 lower case letters of the English alphabet contain:
a) exactly one vowel? b) exactly 2 vowels?
c) at least 1 vowel? d) at least 2 vowels?
5) How many ways are there to select 12 countries in the United Nations to
serve on a council if 3 are selected from a block of 45, 4 are selected from a block
of 57, and the others are selected from the remaining 69 countries?
6) Suppose that a department contains 10 men and 15 women. How many
ways are there to form a committee with 6 members if it must have more women
than men?
7) How many liscence plates consisting of three letters followed by three digits
contain no letter or digit twice?
8) In the women’s tennis tournement at Wimbledon, two finalists, A and B, are
competing for the title, which will be awarded to the first player to win two sets.
In how many different ways can the match be completed?
9) In the men’s tennis tournement at Wimbledon, two finalists, A and B, are
competing for the title, which will be awarded to the first player to win three
sets. In how many different ways can the match be completed?
10) In how many different ways can a panel of 12 jurors and 2 alternate jurors
be chosen from a group of 30 prospective jurors?