Counting Problems Practice
1) In Arizona, a license plate consists of 3 digits followed by 3 letters. Each digit or letter may be used more than once. How many different license plates are possible?
2) In Utah, a license plate consists of 3 digits followed by 3 letters. The letters I, O, and Q are not used, and each digit or letter may be used more than once. How many different license plates are possible?
3) In California, a license plate has this form:
______- ______- ______
any digit any three letters except for “O” any three digits from 0 to 9
from 0 to 9
a) How many different license plates can be created under this system, when letters or digits may repeat?
b) How many different license plates can be created under this system, when letters or digits may not repeat?
4) Use the sentence: MY SHOELACE IS UNTIED. How many arrangements of all the words are possible?
5) Using the word MAINE, how many different permutations are there of all the letters in the word?
6) There are 22 members of the Mathletes. How many ways can the Mathletes select a president, vice president and treasurer?
7) The Mathletes decide that it is not necessary for the officers to have separate rolls. In how many ways can the Mathletes select 3 class officers? (There are still 22 members)
8) How many identification codes are possible by using 3 letters if no letter may be repeated?
9) Suppose you have 7 points on a line. Find the number of ways you can determine the slope of that line.
10) A teacher wants to send 4 students to the library to print out notes for the class. If there are 30 students in the class, how many ways can she choose 4 students to go the library?
11) A teacher is passing out 1st, 2nd, and 3rd place prizes for the best student actor in a production of Hamlet. If there are 18 students in the class, in how many different ways can the awards be presented?