question_answer

Three distinct integers are randomly selected from the set of integers from 16 to 30 (both inclusive). Probability that their sum is even, is

A)  \[\frac{1}{2}\]                         

B)  \[\frac{32}{65}\]

C)  \[\frac{33}{65}\]                                  

D)  \[\frac{3}{5}\]

Correct Answer: B

Solution :

\[8=(a+b+c)\,\] is even   \[P(E)\,=P\] (all 3 even or 2 odd and even) \[=\frac{^{8}{{C}_{3}}\,{{+}^{7}}{{C}_{2}}{{.}^{8}}{{C}_{1}}}{^{15}{{C}_{3}}}\,=\frac{8.7.6}{15.14.13}\,+\frac{21.8.6}{15.14.13}\] \[=\frac{8}{65}\,+\frac{24}{25}=\frac{32}{65}\]