Permutations and Combinations Questions and Answers

There are 30 students in a high school senior class. In how many ways could the yearbook choose the winners of Most Athletic, Class Clown, and Best School Spirit?

Customer account "numbers" for a certain company consists of 4 letters followed by 3 single-digit numbers. How many different account numbers are possible if repetitions of letters and digits are allowed?

In a high school basketball team there are 12 students competing to start a game. If 5 students can be chosen to start a game, how many different starting lineups can be formed from this group of 12 students? 3,991,680 95,040 120 792

Please show all the work that you go through in order to complete the problems. 1. As part of an exercise in an elementary school reading class, the students are given 6 cards that each contain a picture and part of a story. The students are asked to put the cards into an order that tells a coherent story. If a student didn't understand the assignment and had no idea what the intended order was, how many different possible ways could that student choose to place the cards down in order?

For a certain website, your password must be 10 digits long. If the first 8 digits are any numbers and the last 2 digits are any lower case letters, how many passwords are possible? 67,600,000,000 5,200,000,000 67,600 4,160

There were 24 students running in a race. How many different arrangements of first, second, and third place are possible?

How many different license plates can the State of lowa produce if the requirements are as follows: 5 slots The first two slots are for letters. The next three slots are for digits from 0 - 9. 1, 240,000 676,000 82 1,757, 600

A combination for a keypad is 6 digits long. The digits are from 0-9. The same digits MAY NOT be used more than once. How many different combinations are there? 54 1,000,000 60 151, 200

A lock has a 3-number code made up of 20 numbers. If none of the numbers are allowed to repeat, how many different ways can you choose three different numbers in order for a unique code?

Lorena has a bag containing 5 marbles of different colors to use for a statistics experiment. She asks a person to pull out 2 marbles, one at a time, without replacing them. Then she tallies the colors chosen. How many pairs of colored marbles are there?

(6 points) This test contains a total of 7 multiple choice questions, and each multiple choice question features 5 possible answers. (Someone guessing all "a's." for example, would have a string of multiple choice answers that reads "aaaaaaa.") How many strings of multiple choice answers are there that have "e" as the first choice? (b) 6 (c) 6 (d) 57-1 (e) 5

In 2010, the state of Nevada had two area codes. The first three are the area code and the next seven are the local telephone number. (Note that at this time, a local telephone number cannot begin with 0 or 1) How many telephone numbers could Nevada's phone system have accomodated?

In Pennsylvania, each standard automobile license plate number consists of three letters followed by a four-digit number. How many distinct Pennsylvania license plate numbers can be formed?

How many three digit numbers can be formed under each condition? a) The leading digit cannot be 0. b) The leading digit cannot be 0 and no repetition of digits is allowed. c) The leading digit cannot be 0 and the number must be a multiple of 5.

Evaluate 6C3 10 20 18 15

A college student is preparing a course schedule for the next semester. The student must select one of two mathematics courses, one of three science courses, and one of five courses from the social science and humanities. How many schedule are possible?