guys help me with problem solving questions based on permutations and combinations?

Question

1.in how many ways can five books be arranged on a shelf?
(order is important)
tell me how to set this up
(permutation)

2.In how many ways can three students council members be elected from five candidates?(order is not important)
tell me how to set this up (combination)

Answer 1

1.in how many ways can five books be arranged on a shelf?
(order is important)
tell me how to set this up
(permutation)

5x4x3x2x1 = 5!

2.In how many ways can three students council members be elected from five candidates?(order is not important)
tell me how to set this up (combination)
5x4x3/ 3x2x1=10 .

Answer 2

1) 5 choices for the first book, times 4 for the second * 3 * 2 * 1
The answer is 120. The notation for this is 5! (five factorial)
6! = 6x5x4x3x2x1 7! = 7x6x5x4x3x2x1 (etc...)

2) Five choices for the first X Four choices for the 2nd X Three choices for the third. This yields 60 combinations with order being important. For any 3 individuals, there are 6 arrangements (3!), so divide 60 by 6, and you get: Ten possible student councils.