Combination question

[Dhruvil]

In how many ways can we arrange the letters in the word '' ARRANGEMENT" such that
1.) there are exactly 2 consecutive same letters .

Can anyone verify my solution ?

I got : 6*(9!/2!*2! - (8!/2! + 8!/2! - 7!)) Answer

My solution :

 

[Dr.Peterson]

In how many ways can we arrange the letters in the word '' ARRANGEMENT" such that
1.) there are exactly 2 consecutive same letters .

Can anyone verify my solution ?

I got : 6*(9!/2!*2! - (8!/2! + 8!/2! - 7!)) Answer

My solution :

The problem is a little ambiguous; I read it as saying that exactly one pair of consecutive letters are the same, while you are taking it as two pairs. I'll assume that you are interpreting it as you were taught to, as English usage does vary around the world; but you may want to check.

Given that interpretation, it looks good to me.

 

[Dhruvil]

Sir actually I get this question from below site and they have diff answer i.e : 7! Sign is different

inclusion exclusion principle / GATE Overflow for GATE CSE

In how many ways can we arrange the letters in the word '' ARRANGEMENT" such that 1.) there ... letters . 2.) atleast 3 consecutive same letters .

gateoverflow.in

My answer
6*(9!/2!*2! - (8!/2! + 8!/2! - 7!))

Answer in site
6*(9!/2!*2! - (8!/2! + 8!/2! + 7!))

Now can you verify which is correct ?

 

[Dr.Peterson]

Sir actually I get this question from below site and they have diff answer i.e : 7! Sign is different

inclusion exclusion principle / GATE Overflow for GATE CSE

In how many ways can we arrange the letters in the word '' ARRANGEMENT" such that 1.) there ... letters . 2.) atleast 3 consecutive same letters .

gateoverflow.in

My answer
6*(9!/2!*2! - (8!/2! + 8!/2! - 7!))

Answer in site
6*(9!/2!*2! - (8!/2! + 8!/2! + 7!))

Now can you verify which is correct ?

I don't see any one final answer from a person I would trust.

But I suspect that they meant

6*(9!/2!*2! - (8!/2! + 8!/2!) + 7!)​

This is the way you would think of it in light of the inclusion-exclusion principle.