Define and use permutations.

How many 4-character passwords can be formed using digits from {1, 2, 3, 4, 5, 6} without repetition?

A password system requires users to create a 5-character code using 5 different digits selected from 1, 2, 3, 4, 5, 6, 7. How many such passwords can be formed?

A password system requires users to create a 5-character code using 5 different digits selected from {1, 2, 3, 4, 5, 6, 7}. Each password must include both the digit 3 and the digit 7, with 3 appearing before 7 (though not necessarily immediately before). Calculate the number of possible passwords.

How many 5-digit codes can be formed using five different digits from the set {1, 2, 3, 4, 5, 6, 7} if both 3 and 7 must appear, and 3 must come before 7?

A bookshelf contains 5 mathematics textbooks, 3 physics textbooks, and 2 chemistry textbooks. The books are to be arranged in a row such that all books of the same subject are grouped together. Determine the number of different arrangements possible.

A password consists of 4 different digits selected from {1, 2, 3, 4, 5, 6}. How many such passwords are possible?

A technology company assigns each employee a unique 8-digit access code. The code must begin with 3, end with an even digit, and use only the digits 2, 3, 4, 5, 6, 7, 8 (with repetition allowed). a) Determine the number of distinct access codes that can be created under these constraints. (2 marks) b) Use your result from part (a) to determine the probability, correct to three decimal places, that a randomly selected code contains the digit 5 in the second position. (1 mark)

How many different 4-digit codes can be formed using the digits 1, 2, 3, 4, 5 if no digit may be repeated?

A password consists of 5 different digits selected from {1, 2, 3, 4, 5, 6, 7}, and must include both the digit 3 and the digit 7. How many such passwords have the digit 3 appearing before the digit 7?