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  4. Number of ways in which three distinct numbers can be chosen from the set 1,2,3,4,5,6,7,8,9,10 such that a < b < c and c - b = b - a, is

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Q. Number of ways in which three distinct numbers can be chosen from the set $\{1,2,3,4,5,6,7,8,9,10\}$ such that $a < b < c$ and $c - b = b - a$, is

Permutations and Combinations

Solution:

$ S _1=\{1,3,5,7,9\}$
$S _2=\{2,4,6,8,10\} $
$\therefore{ }^5 C _2+{ }^5 C _2=20 $