Question

If all permutations of the letters of the word "BEFORE" are arranged in the order as in a dictionary. What is the 32 word?

Answer 1

Distinct letters of the given word in dictionary order ={B, E, F, O, R}

Total number of letters =6 (say, 6 boxes).

No. of distinct letters =5 (B, E, F, O, R).

No. of repeated letters =2 (E, E).

So, the 6 boxes has to be filled with 6 letters in which two letters are the same (E, E).

No. of letters stating with B =5! =120

So, it's difficult to find 32^nd word unless we write all 32 words in dictionary order with or without meaning.

No. of letters starting with BE =4! =24

(since after filling BE, we are left 4 boxes that are filled using the letters F, O, R, E).

No. of words starting with BF =4!/2! =24/2 =12

(since after filling BF, we are left with 4 boxes that are filled using the letters O, R, E, E. The letter E is repeated twice and so, we divide 4! by 2!).

Till now we have 24+12 =36 words but we need 32^nd word. So, let's write last five words of these 36 words which have to be written in reverse dictionary order in order to get 32^nd word.

36. BFROEE

35. BFREOE

34. BFOREE

33. BFOERE

32. BFEROE

So, 32^nd word is BFEROE

Or we can write it as: Bferoe