Why can’t the problem with “Bobbie” be solved like the latter?
My writing is pretty bad, but hopefully, you’ll get it.
Hey @user3156 ,
I think you are not applying the logic consistently. For the word “BOBBIE”, you see you wrote (3!/3!)x3! here 3! in the numerator for the block is incorrect because we are treating BBB as one block so consider this as letter y for now and we are left with 3 other letters that are OIE so that means 4 letters in total to arrange so this would also be 4!. What you have done is consider only 3 letters. You see the error?
For AMERICA, on the other hand, AAEI is one block so consider this as one letter y so we are left with M,C,R so in total 4! so that approach also uses 4 letters as opposed to 3 like you did for “BOBBIE” so means the second method you adopted is incorrect because it is considering only 3 letters.
Hope it makes sense. Let me know if this still unclear.
Thanks for explaining. I still have doubts. If I consider AAEI as Block Y in America, Then for YMCR shouldn’t the answer be 4!/2! only? Where does the 3! come from then?
I interpreted it as, since the question says that vowels must be at first , I separated the vowels at first and did repeat permutations for the 4 vowels since the vowels can rearrange among themselves, which gave 4!/2! and 3! came from MCR.
can you share the exact question text or a screenshot of the question? Because I think If all vowels are a one block AAEI and MCR are separate. Answer should be 4! x (4!/2!) because within the vowel block AAEI will also permutate in 4!/2! ways (2! for the repetition of AA). So, I think the solution itself is flawed but I could be wrong too that is why i am asking you to share question text
or
It could also mean that if the question requires that vowel block should come first then you can arrange that in only 3! ways because
1__ 3 _2 _1
(vowel block) (MCR)
You see because we have to put vowel block at first and then MCR can be arranged in 3! ways. It depends on the question text so your reasoning about 3! isn’t wrong. In the case of BOBBIE, question doesn’t require BBB block to come first. It just wants them to come together that is they are treated differently
I will circle back to this. Because question requires vowel block to be put first that is why it is 3! as you interpreted and for the same reason we can’t solve the word “BOBBIE” with a similar approach because there is no requirement to put BBB at first place. They just need to be together.
Hope this makes sense now
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I get it now. Then If there was a requirement for BBB to be in the first place, what would be the answer? 3! ?
Yes precisely
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Thanks for helping me out. I hate Permutations and Combinations, as u can prolly guess.
No problem. I understand. They can get really nasty sometimes. Glad to know it is clear now. 
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