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National and Regional Contests
Bulgaria Contests
Bulgaria National Olympiad
1980 Bulgaria National Olympiad
Problem 5
Problem 5
Part of
1980 Bulgaria National Olympiad
Problems
(1)
choose 6 integers, 2 consecutive, out of [49]
Source: Bulgaria 1980 P5
6/17/2021
Prove that the number of ways of choosing
6
6
6
among the first
49
49
49
positive integers, at least two of which are consecutive, is equal to
(
49
6
)
−
(
44
6
)
\binom{49}6-\binom{44}6
(
6
49
)
−
(
6
44
)
.
combinatorics