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Let \bigcup_{i=1}^{50}X_{i}=\bigcup_{i=1}^{n}Y_{i}=T, where each Xi contains 10 elements and each Yi contains 5 elements. If each element of the set T is an element of exactly 20 sets X_{i}'s and exactly 6 sets Y_{i}'s then n is equal to:
Option: 1 15
Option: 2 50
Option: 3 45
Option: 4 30

Answers (1)

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\\n\left(X_{i}\right)=10\\ \bigcup_{i=1}^{50} X_{i}=T, \Rightarrow n(T)=500

each element of T belongs to exactly 20 elements of Xi

\Rightarrow \frac{500}{20}=25 \text { distinct element }

\text { so } \frac{5 \mathrm{n}}{6}=25 \Rightarrow \mathrm{n}=30

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himanshu.meshram

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