Combination and Permutation

Question

A professor grades homework by randomly checking 9 of the 25 problems assigned. In how many different ways can this be done?

How many words can be formed from the letters of the word computer if each letter is to be used once?

If there are 8 class periods in a school day, and a typical student takes 4 classes, how many different time patterns are possible for the student?

If a customer purchases a new stereo system during the spring sale, he may choose any 4 CDs from 22 classical and 30 jazz selections. In how many ways can the customer choose 2 of each?

Answer 1

combination

25 choose 9

n!/r!(n-r)!

25!/9!*(25-9)!

25!/9!*16!

(25*24*23*22*21*20*19*18*17)/(9*8*7*6*5*4*3*2*1)

25*23*11*19*17=2,042,975  ways  (after simplifying)

 

permutation

computer has 8 letters

8!=8*7*6*5*4*3*2*1=40,320

 

combination

8 choose 4

8!/4!(8-4)!

8!/4!*4!

(8*7*6*5)/(4*3*2*1)

70 time patterns

 

combination

22 choose 2 and 30 choose 2

22!/2!20!=(22*21)/2=11*21=231

30!/2!28!=(30*29)/2=15*29=435

231*435=100,485 ways