Suppose are thirty sets each having 5 elements and are sets with 3 elements each. Let and each element of belongs to exactly 10 of the s and exactly 9 of the s. Then is equal to:

45 Explanation: Step 1: Calculate the total number of elements in all sets combined Since there are 30 sets ( to ) and each has 5 elements: Step 2: Find the number of distinct elements in Set using It is given that each element of belongs to exactly 10 of the sets. If is the number of elements in : So, the set contains 15 distinct elements. Step 3: Calculate the total number of elements in all sets combined There are sets ( to ) and each has 3 elements: Step 4: Find the number of distinct elements in Set using It is given that each element of belongs to exactly 9 of the sets. Since we know has 15 elements: Substitute : Step 5: Solve for Final Answer: The value of is 45 . The correct option is (c) .

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NIMCET 2008 — Mathematics PYQ

NIMCET | Mathematics | 2008

Suppose $P_1, P_2, \dots, P_{30}$ are thirty sets each having 5 elements and $Q_1, Q_2, \dots, Q_n$ are $n$ sets with 3 elements each. Let $\bigcup_{i=1}^{30} P_i = \bigcup_{j=1}^{n} Q_j = S$ and each element of $S$ belongs to exactly 10 of the $P_i$ s and exactly 9 of the $Q_j$ s. Then $n$ is equal to:

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NIMCET 2008 — Mathematics PYQ

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