Question-2

A professor is creating an exam of eleven questions from a test bank of 15 questions. In how many ways can he select and arrange the questions?

• \(15!\)
• \(15! / 11! 4!\)
• \(15! / 11!\)
• \(15! / 4!\)

Hint

Use the concept of permutation.

Answer

Toggle the appropriate answers.

• \(15!\)
• \(15! / 11! 4!\)
• \(15! /11!\)
• \(15! / 4!\)

Solution

Professor can select 11 questions from a test bank of 15 questions in \(^{15}C_{11}\) ways and he can arrange in \(11!\) ways. So, number of ways in which he can select and arrange the questions is \(^{15}C_{11} \times 11! = ^{15}P_{11} = \dfrac{15!}{4!}\).