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Let $\mathrm{A}=\{1,2,3,4,5,6,7,8,9,10\}$. Then the number of subsets of A containing two or three elements is
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The correct answer is:
165
Given, A $\{1,2,3,4,5,6,7,8,9,10\}$ Set $\mathrm{A}$ has 10 elements. Number of sub sets Containing 2 and 3 elements is
${ }^{10} \mathrm{c}_{\mathrm{c}}+10_{\mathrm{c}_{3}}$
$10_{\mathrm{c}_{2}}+10_{\mathrm{c}_{3}}=\frac{10 \times 9}{2}+\frac{10 \times 9 \times 8}{3 \times 2}$
$=45+120=165$
${ }^{10} \mathrm{c}_{\mathrm{c}}+10_{\mathrm{c}_{3}}$
$10_{\mathrm{c}_{2}}+10_{\mathrm{c}_{3}}=\frac{10 \times 9}{2}+\frac{10 \times 9 \times 8}{3 \times 2}$
$=45+120=165$
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