8.02 Permutations
Evaluate the following expressions:
5!
\dfrac{7!}{5!}
{}^{6}P_{3}
{}^{5}P_{5}
{}^{4}P_{0}
{}^{11}P_{1}
{}^{7}P_{3}
{}^{8}P_{6}
How many ways can 9 different items be arranged in a line?
Five cards have different letters written on them. The letters are M, L, I, E, S. The cards are shuffled and laid out on a table with the letters face up next to one another. How many possible arrangements are there?
How many different ways can the letters of the word 'SHELF' be arranged?
If there are 5 swimmers in a race, in how many different orders can they finish (assuming there are no ties)?
In how many ways can 4 women and 5 men enter a lifeboat if women are to enter first?
If an mp3 player contains 7 songs, in how many different ways could all 7 songs be played, with no song being repeated?
To determine the successful applicant for a job, the interviewer assigns a problem at random to each applicant. If there are 4 applicants, how many different ways can the problems be assigned among them?
In the qualifying round of a car race, the 8 cars are given random starting positions. In how many different ways can starting positions be allocated?
An exam consists of 8 multiple choice questions, where the correct answer could be \text{A, B, C} or \text{D} . If the answer to each question is guessed randomly, how many different ways are there of answering all 8 questions?
Katrina's ATM pin is a 4-digit number. She remembers the first digit, but cannot remember the next three digits that follow. How many different possibilities are there?
Motorists can create personalised licence plates consisting of 6 characters, and they can be arranged in any way the motorist chooses.
Tina wants to use her three favourite letters \text{L, Y} and \text{X}, and her three favourite digits, 6, 9 and 1.
How many different licence plates can she create if the letters and digits can appear in any particular order (and no character can be repeated)?
How many different licence plates can she create if the three letters are followed by the three digits (and no characters can be repeated)?