MathDB
choose 6 integers, 2 consecutive, out of [49]

Source: Bulgaria 1980 P5

June 17, 2021
combinatorics

Problem Statement

Prove that the number of ways of choosing 66 among the first 4949 positive integers, at least two of which are consecutive, is equal to (496)−(446)\binom{49}6-\binom{44}6.
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