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If a set $\mathrm{X}$ contains $\mathrm{n}(\mathrm{n}>5)$ elements, then what is the number of subsets of $X$ containing less than 5 elements?
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The correct answer is:
$\sum_{r=0}^{4} C(n, r)$
Number of subsets of $\mathrm{X}$ containing less than 5 elements is given by
${ }^{\mathrm{n}} \mathrm{C}_{0}+{ }^{\mathrm{n}} \mathrm{C}_{1}+{ }^{\mathrm{n}} \mathrm{C}_{2}+{ }^{\mathrm{n}} \mathrm{C}_{3}+{ }^{\mathrm{n}} \mathrm{C}_{4}$
$\sum_{\mathrm{r}=0}^{4}{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}=\sum_{\mathrm{r}=0}^{4} \mathrm{C}(\mathrm{n}, \mathrm{r})$
${ }^{\mathrm{n}} \mathrm{C}_{0}+{ }^{\mathrm{n}} \mathrm{C}_{1}+{ }^{\mathrm{n}} \mathrm{C}_{2}+{ }^{\mathrm{n}} \mathrm{C}_{3}+{ }^{\mathrm{n}} \mathrm{C}_{4}$
$\sum_{\mathrm{r}=0}^{4}{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}=\sum_{\mathrm{r}=0}^{4} \mathrm{C}(\mathrm{n}, \mathrm{r})$
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