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

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

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