Question

The number of three element subsets of $\{1,\mathrm{2.....10}\}$ sum of whose elements is even is

• A. $50$
• B. $60$
• C. $70$
• D. $90$

Answer 1

Answer: (B)

$60$

There are $5$ even $\xi$ $5$ odd numbers in the given set.

We know that sum of any number of even numbers is always even $\xi$ sum of even numbers of odd numbers is always even.

$\Rightarrow$ Different possibilities-

even $+$ even $+$ even $=$ even

odd $+$ odd $+$ even $=$ even

$\Rightarrow$ Combination $={}^5{C}_3+{}^5{C}_2\times {}^5{C}_1$

$=10+(10\times 5)$

Total $=60$

Hence, the answer is $60.$