The number of substrings (both trivial and nontrivial included) for a string containing n distinct characters isa)b)c)d)Correct answer is option 'D'. Can you explain this answer?

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The number of substrings (both trivial and nontrivial included) for a string containing n distinct characters is

Correct answer is option 'D'. Can you explain this answer?

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The number of substrings (both trivial and nontrivial included) for a...

This is how we derive the number of substrings in a string of n characters. Substrings containing 0 letters = 1(ϵ)

1 letters = n

2 letters = n − 1

3 letters = n − 2

(n − 1) letters = 2

n letters =1

Add then up, 1 + (n + m − 1 + n − 2 +…….+ 3 + 2 + 1)

=1 + [n(n + 1)2]

Hence (d) is the most appropriate choice.

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