# Problem Solving With Permutations

1. Feb 20, 2012

### koolkidx45

Hi, I have the following questions

1) A coin is tossed 9 times. In how many ways could the results be six heads and three tails?

2) A man bought two vanilla ice cream cones, three chocolate ones, four strawberry, and one butterscotch. In how many ways could he distribute them among his 10 children?

3) Juan's soccer team played a total of 14 games this season. Their record was eight wins, four losses, and two ties. In how many orders could this have happened?

I think for the above problems you take the total factorial and divide by the duplicate factorials. For ex for 1) 9! / 6! x 3! = 84

Any help is appreciated. Thanks!

2. Feb 20, 2012

### tiny-tim

3. Feb 20, 2012

### Ray Vickson

Your answer is correct for 1). Now, how would you do 2) or 3)? Hint for 3): think of it in two stages: first count the number of ways of having 8 wins and 6 non-wins. Then, for each such way, break up the 6 non-wins into 4 losses and 2 ties.

RGV