inclusion exclusion principle

Question

In how many ways can we arrange the letters in the word '' ARRANGEMENT" such that

1.) there are exactly 2 consecutive same letters .

2.) atleast 3 consecutive same letters .

Comments

because in 8!/2! we are already including the case where all 4 consecutive letters appear. we are adding it three times so we need to subtract it 2 times so that it gets added once.

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3 * (8!/2!) + 7!

Is my approach is right ????

it should be  3 * (8!/2!-7!) + 7!

check it once

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sushmita yeah understood thank you :)