Permutations of N Things: Different

How many different positive integers of 2 digits each can be made with the digits 2, 4, 5, and 8, if no digit is repeated in a number?

12

Compute the permutation 5P4

120

Compute the permutation 5P5

120

Compute the permutation 9P5

15,120

Compute the permutation 8P4

1680

A farmer has 4 fields to plow. In how many different orders can he do the plowing?

24

Compute the permutation 30P3

24,360

Compute the permutation 3P1

3

Compute the permutation 8P3

336

How many positive integers of 3 digits each can be formed with the digits 1, 8, 9, 2, 7, 6, 4, and 3, if no digit is repeated in a number?

336

How many ways can 8 books be arranged on a shelf? Show all of your work for full credit.

8!=8(7)(6)(5)(4)(3)(2)(1)=40320

A 5-digit combination lock with digits 0-9 can be opened only if a correct combination of digits is chosen. Find the probability of guessing the correct combination if: A. no digit is repeated B. digits can repeat and zero is not one of the digits in the combination

A. 1/30240 B. 1/59049

The letters of the word COMBINE are placed at random in a row. In how many ways can an arrangement occur such that all vowels are placed together? Show all of your work for full credit.

Since there are 7 letters and 3 vowels in the word combine, the permutation would be 7P3. When you plug it into the equation n!/(n-r)! you get 7!/(7-3)!=7!/4!=5040/24=210

The question, "How many ways can 4 students be chosen from a class of 30 students?", is a(n) _____.

permutation

Compute the permutation 6P4

360

A chemist has eight test tubes to examine. In how many orders can he do this examination?

40320

Compute the permutation 7P2

42

Compute the permutation 7P7

5040