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The letters of the word RACKET are arranged in all possible ways. All the woods thereby formed are arranged as in a dictionary. The word which has a rank of 104 from the end is?
Hi
We have word RACKET
The total words that can be formed = 6!=720
Now we have to find the 104th term from end
so 720+(n-1)d
=720+(103)(-1)=617
so we have to find 617th word from start
Now we will start alphabetically
So we will fix A so we will get 5! words =120 words
Now C,K,E,T will also give 5!=120 words
so total 600 words will be completed till we finish R
NOw 601st words will be starting from T and it will be TACEKT
Now We will fix TA so CEKT can be arranged in 4! ways so we will get 24 words now total becomes 600+24=624 but we want 617
so we can conclude the 2nd letter will be A
Now we will fix TAC so KER will be arranged in 3! ways =6 ways so we get 606 words
Now we will fix TAE so we will again get 6 ways Now we have reached till 612.
Now we will fix TAK so CER will be arranged in 6 ways again and we will reach to total 618 words
so 618th word will be TAKREC
Now we need 617th word so in 617th E and C will interchange their position
so we get 617th word as TAKRCE
The word which has a rank of 104 from the end has a rank of 617 from the beginning.
Answer: TAKRCE
