Testbook Test Series: Combinatory - Permutations And Combinations

Question

Number of ways of arranging the word "TESTBOOK" such that E always comes between O's.

Comments

I am getting 2160

6(5*(5¦/2)) + 6¦/2

Correct me where I am wrong

Answer 1

O    E   O
The rest of the  letters T,S,T,B and K can come before  first O,Between first O and E, between E and second O and after second O.
For now consider both T as distinct, T1 and T2
Place T1 there are _O_E_O_ 4 places
now a new space is created, for eg if we put T1 at end then _O_E_O_T1_
If somewhere in middle then _O_T1_E_O_
As you can see 5 places for S
Similarly 6 places for T2
7 places for B and 8 places for K
Hence 4*5*6*7*8
Since T1 and T2 are same when interchanged
4*5*6*7*8/2=3360
 

Comments

 @Shaik Masthan i guess this will be more apt . as question is ambiguous so this would be more generalized approach

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@TUSHAR what was the answer in testbook?

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yeah this is the answer only
but was not getting their approach yours is better

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@TUSHAR_BHATT

i agree, i mis-understood the question.

Answer 2

check this

Comments

yes I'm also done this way

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Shaik It's testbook .you write textbook ;)

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@Rustam Ali

i didn't observe it., Thanks for that

Answer is same, just we have to replace x by s.

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@ Shaik Masthan there can also be cases when e and other letters are also in between O's