Question

english has 26 different letters. how many consecutive words have to be selected in a book to have at least 5 that start with the same letter?

Answer 1

The words need not be English language words  142506

What is permutation and combination?

A set of elements can be divided into subsets in two different ways: combination and permutation.

                          The components of the subset may be arranged in any order when combined. The components of the subset are listed in a permutation in a certain order.

If the word has 5 different letters  then it is just 26-choose-5 or (26/5).

If the word has 4 different letters  then it is just 26-choose-4 or (26/4)

have 4 options to choose which letter to duplicate twice.

This gives =  4*(26/4)

If the word has 3 different letters  then it is just 26-choose-3 or (26/3).

you duplicate one of the three letters 3 times - 3 options for that, or you choose 2 letters and duplicate each one twice - again 3 options. In total this gives  = 6*(26/3).

If the word has 2 different letters  then it is just 26-choose-2 or (26/2).

The sets of 2 different letters and duplicate either one of the letters 4 times - 2 options; or duplicate one letter 2 times, and the other 3 times - again 2 options. In total this is  = 4*(26/2).

The word has just 1 distinct letter you have =  (26/1).

we get :

N = (26/5)+ 4*(26/4) + 6*(26/3) + 4*(26/2) +  (26/1)

= 142506

The words need not be English language words  = 142506

Learn more about  permutation and combination

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