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  4. Number of ways in which three distinct numbers can be selected between 1 and 20 both inclusive, whose sum is even is

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Q. Number of ways in which three distinct numbers can be selected between 1 and 20 both inclusive, whose sum is even is

Permutations and Combinations

Solution:

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${ }^{10} C _3+{ }^{10} C _1 \cdot{ }^{10} C _2=120+450=570$.