7P7 Permutation

Question: The question, "How many ways can 4 students be chosen from a class of 30 students?", is a(n) _____.
Answer: permutation
==================================================
Question: Compute the permutation
7P2
Answer: 42
==================================================
Question: Compute the permutation
30P3
Answer: 24,360
==================================================
Question: Compute the permutation
5P5
Answer: 120
==================================================
Question: Compute the permutation
8P3
Answer: 336
==================================================
Question: Compute the permutation
9P5
Answer: 15,120
==================================================
Question: Compute the permutation
7P7
Answer: 5040
==================================================
Question: Compute the permutation
6P4
Answer: 360
==================================================
Question: Compute the permutation
8P4
Answer: 1680
==================================================
Question: Compute the permutation
5P4
Answer: 120
==================================================
Question: Compute the permutation
3P1
Answer: 3
==================================================
Question: A farmer has 4 fields to plow. In how many different orders can he do the plowing?
Answer: 24
==================================================
Question: How many ways can 8 books be arranged on a shelf? Show all of your work for full credit.
Answer: 8!=8(7)(6)(5)(4)(3)(2)(1)=40320
==================================================
Question: 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?
Answer: 12
==================================================
Question: 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?
Answer: 336
==================================================
Question: A chemist has eight test tubes to examine. In how many orders can he do this examination?
Answer: 40320
==================================================
Question: 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
Answer: A. 1/30240
B. 1/59049
==================================================
Question: 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.
Answer: 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
==================================================