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Question: Answered & Verified by Expert
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?
MathematicsSets and RelationsNDANDA 2006 (Phase 2)
Options:
  • A $\mathrm{C}(\mathrm{n}, 4)$
  • B $\bar{C}(\mathrm{n}, 5)$
  • C $\sum_{r=0}^{5} \mathrm{C}(\mathrm{n}, \mathrm{r})$
  • D $\sum_{r=0}^{4} C(n, r)$
Solution:
1893 Upvotes Verified Answer
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
${ }^{\mathrm{n}} \mathrm{C}_{0}+{ }^{\mathrm{n}} \mathrm{C}_{1}+{ }^{\mathrm{n}} \mathrm{C}_{2}+{ }^{\mathrm{n}} \mathrm{C}_{3}+{ }^{\mathrm{n}} \mathrm{C}_{4}$
$\sum_{\mathrm{r}=0}^{4}{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}=\sum_{\mathrm{r}=0}^{4} \mathrm{C}(\mathrm{n}, \mathrm{r})$

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