Counting

Question 1

Number of substrings in a string

Answer 1

For first char it will be n,
For second char it will be n - 1,
For third char it will be n - 2,
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.
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1 - String with all chars, actual string
So it is addition of all n + (n - 1) + (n - 2) + ... + 1 = n (n+1) / 2

Question 2

In world cup there are 10 teams, all teams will play others. How many matches will be there?

Answer 2

10 C 2 = 10! / (8! * 2!) = 90 / 2 = 45