Question:
Write the value of $\left({ }^{5} C_{1}+{ }^{5} C_{2}+{ }^{5} C_{3}+{ }^{5} C_{4}+{ }^{5} C_{5}\right)$
Solution:
$\Rightarrow{ }^{5} \mathrm{C}_{1}+{ }^{5} \mathrm{C}_{2}+{ }^{5} \mathrm{C}_{3}+{ }^{5} \mathrm{C}_{4}+{ }^{5} \mathrm{C}_{5} \Rightarrow{ }^{6} \mathrm{C}_{2}+{ }^{6} \mathrm{C}_{4}+1\left[\right.$ As $\left.{ }^{5} \mathrm{C}_{5}=1\right] \Rightarrow 15+15+1 \Rightarrow 31$
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