@Tushar_Rathore

What is the general formula bro?

# Doubt from Permutations and combination

**Tushar_2019**#22

ordering x elements of a string of y elements such that none of the x elements are next to each other has {y-x+1\choose x}

@Viraam_Rao

**Mayank_2019_1**#32

Finally gotcha !

See here consider the flagpoles one on top of the other. So we basically have a line of flags where we need to cut at any place so that we get two flagpoles.

Case 1:

First according to the given conditions, I place 10 blues, we have 11 gaps so we get 11C9 no. of ways of doing so. Now we have 18 places to cut (note that since we have 19 flags and each flagpole contains at least one flag we have 18 places)

So total : 11C9× 18 = 55 × 18

Case 2:

Now in the above procedure we have left the cases where there are two green flags adjacent to each other and we can cut in between the two Green flags in order to avoid violation of the given condition.

So again we first put 10 blue flags this creating 11 gaps and now we choose 1 out of 11 gaps for two green flags. Hence we are now left with 9-2=7 green flags and 11-1=10 gaps. So we 10C7

So total : 11C1 × 10C7

Adding both we get the result