Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XI  >>  Math  >>  Permutations and Combinations
0 votes

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

$\begin{array}{1 1}(A)\;455\\(B)\;1575\\(C)\;1120\\(D)\;2030\end{array} $

Can you answer this question?

1 Answer

0 votes
  • $C(n,r)=\large\frac{n!}{r!(n-r)!}$
Number are either all even or one even and other two odd.
Required number of ways =$15C_3+15C_1\times 15C_2$
$15C_3=\large\frac{15!}{3!12!}=\frac{15\times 14\times 13\times 12!}{3\times 2\times 12!}$
$\Rightarrow 455$
$15C_1=\large\frac{15!}{1!\times 14!}$
$\Rightarrow 15$
$15C_2=\large\frac{15!}{2!\times 13!}$
$\Rightarrow 105$
$15C_3+15C_1\times 15C_2=455+15\times 105$
$\Rightarrow 455+1575$
$\Rightarrow 2030$
Hence (D) is the correct answer.
answered Jun 20, 2014 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App