00:01
Snow white arranges the seven dwarfs around a maypole.
00:06
In how many ways can she do it if grumpy and dopey must not be together? right? so the total number of possible arrangements here is factorial 7.
00:36
Why is it so? because order matter at all a lot this is one two three four five six so this is seven ways then six ways is possible then five ways is possible four ways then three then two then this is one okay so this is how we do so this is nothing but this is factorial seven ways so this is very simple for permutation uh like part right we can find out here arrangement and the position matters here okay now the if you are like subtract the arrangement with grumpy and ops together dopey together then you can you can just subtract this from total one then you can find out the value that total arrangements without grumpy and dopey together okay so now there would be therefore you can say total total arrangements without grumpy and dopey together would be equals to, that would be in factorial 6 ways and this is multiplied by factorial 2 ways.
02:01
I will tell you why.
02:02
Okay.
02:03
Suppose there is an arrangement.
02:04
Okay.
02:05
So, this is the arrangement let us make.
02:08
This is 1, 2, 3, 4, 5, 6, 7.
02:14
Right.
02:14
So in all together we will take this to be together because we want to calculate when both are dopey and grumpy are together.
02:25
So this is supposed to be one place.
02:31
Then this is second place.
02:34
Then this is third place.
02:37
Because they are together.
02:38
So we will assume it to be one place.
02:41
Because they cannot be changed.
02:43
Right.
02:43
Right they can interchange each other right so that is another part so this is fourth place this is fourth place this is third place and this is second place and this is first place as i already told this is fifth place and this is sixth place so uh grumpy and dopey can come together here somewhere here or here but they should be together and the another part would be so this this could be rearranged.
03:16
This arrangement could be rearranged in factorial 6 ways.
03:22
And it is multiplied by in how many ways these grumpy and dopey can be rearranged.
03:29
This would be factorial 2 ways, right? because in one time dopey is here then grumpy is afterwards, right? okay...