Question

If a $Set-A$ have $12$ elements, then the number of subsets of $A$ having atleast $3$ elements is

• A. $4017$
• B. $4027$
• C. $4067$
• D. $4087$

Answer 1

The correct option is A $4017$

Suppose $n\left(A\right)=12$

We can write $\left(3\text{element subset}\right)+\left(4\text{element subset}\right)+....+\left(12\text{element subset}\right)$

$=\text{Total subset}-(0\text{element subset}+1\text{element subset}+2\text{element subset})$

$=2^{12}-{(}^{12}{C}_0{+}^{12}{C}_1{+}^{12}{C}_2)$

$=4096-(1+12+66)$

$=4096-79$

$=4017$

Thus option A is correct.