The number of ways in which one can select three distinct integers between 1 and 30, both inclusive, whose sum is even, is

Question

Dr. Abubacker · Accepted Answer

(d)
$\because\$ Number are either all even or one even and other two odd
$	herefore$ Required number of ways $= \ ^{15}C_{3} + \ ^{15}C_{1} 	imes \ ^{15}C_{2}$
$= \frac{15!}{3! 	imes 12!} + \frac{15!}{14!} 	imes \frac{15!}{2! 	imes 13!}$
$= \frac{15 	imes 14 	imes 13}{6} + \frac{15 	imes 15 	imes 14}{2}$
$= 455 + 1575 = 2030$

Q. The number of ways in which one can select three distinct integers between 1 and 30, both inclusive, whose sum is even, is

Explanation

Reviewed by Dr. Abubacker

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