Question

Let $A=\{1,2,3,4,5,6,7,8,9,10\}$. Then the number of subsets of $A$ containing exactly two elements is

• A. $20$
• B. $40$
• C. $45$
• D. $90$

Answer 1

Answer: (C)

$45$

Number of elements in $A=10$

Number of subsets of $A$ containing exactly two elements

$=$ Number of ways we can select $2$ elements from $10$ elements

${}^{10}{C}_2=\frac{10\times 9}{2}=45$

$\therefore$ Number of subsets of $A$ containing exactly two elements $=45$