Question

The maximum number of distinct subwords of the word "AXIOMATIZABLE" is: a)183 b) 111 c)92 d)88

Answer 1

Subwords means letters must be consecutive as in the word. Since, the given word has 13 letters we can have

13 subwords of 1 letter

12 subwords of 2 letters

11 subwords of 3 letters

....
1 subword of 13 letters

So, total number of subwords = 13 + 12 + ... + 1 = 13 * 7 = 91

No two consecutive letters are repeating in the given word. But there are 3 A's, and 2 I's. So, 3 subwords of length 1 are counted extra. So, total number of distinct subwords = 91 - 3 = 88.

Comments

@Jyotsana Bharti

$ n(n+1)/2 = (13*14)/2 $

 

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{n(n-1)/2 }+ x (distinct character)

is it work always?

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can some one tell me why is this approach of mine wrong … GIVEN  the 13 letter word we have 14 spaces between then .. we could choose any of the 2 spaces out of the 14 spaces and thus there would be 14 Choose 2 [ 14 C 2 ] sub words .. is my approach over counting some of the combinations ….. can any one explain .. … . .. . . . … . . . .