# Permutations and Combinations

• May 14th 2007, 08:00 AM
Darky001
Permutations and Combinations
I'm currently having a bit of trouble with some questions, this one in particular. Everytime I try and do it I end up doing some sort of statistic probability, which is not what I need. The question is:

Suppose that a die is tossed ten times and the sequence of upturned numbers is recorded in order

a) How many outcomes are there?
b) How many outcomes are there exactly 3 fours?
c) How many outcomes are there at most 3 fours?

What I have done so far is figured out that there would be 6^10 different possible outcomes, but apart from that I keep going in a loop for b and c. Any help would be appreciated, or any pointers into what I should be looking at doing. :)
• May 14th 2007, 09:38 AM
Plato
Quote:

Originally Posted by Darky001
Suppose that a die is tossed ten times and the sequence of upturned numbers is recorded in order
b) How many outcomes are there exactly 3 fours?
c) How many outcomes are there at most 3 fours?

b) You have ten positions in which to put the fours, choose three of them:
Combin(10,3)(5^7). In the other seven places put any one of five other numbers.

c) Sum{k=0 to k=3}Combin(10,k)(5^{10-k}).
• May 14th 2007, 05:18 PM
Darky001
Ahh thankyou! :D