Permutations/Combinations

In how many permutations can I place flags (red or blue) on the sandbox such that there are 9 flags on the sand box, and there are at least 2 blue flags? Show solution.

 

 

2blue 7red      

 **R*RRRRRR           9C7     

3blue 6red    

***RRRRRR                9C6                     

4blue 5red

****RRRRR                  9C5

5blue 4red

*****RRRR                    9C4

6blue 3red

******RRR                   9C3

7blue 2red

*******RR                       9C2

8blue 1red

********R                        9C1

9blue                               1

 

nCr(9,7)+nCr(9,6)+nCr(9,5)+nCr(9,4)+nCr(9,3)+nCr(9,2)+nCr(9,1)+1

nCr(9,7)+nCr(9,6)+nCr(9,5)+nCr(9,4)+nCr(9,3)+nCr(9,2)+nCr(9,1)+1 = 502

 

So I get 502 ways.