Combinations

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Question

Let A be a set containing ten elements. Then the number of subsets of A containing at least four elements is

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Solution

Required number of subsets
$\begin{array}{l} =^{10} C_{4} +^{10} C_{5} + \dots +^{10} C_{10} \\ = 2^{10} - (^{10} C_{0} +^{10} C_{1} +^{10} C_{2} +^{10} C_{3}) \\ = 1024 - (1 + 10 + 45 + 120) = 848 \end{array}$

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