"Let $$\mathop \cup \limits_{i = 1}^{50} {X_i} = \mathop \cup \limits_{i = 1}^n {Y_i} = T$$ 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 of sets Xi’s and exactly 6 of sets Yi’s, then n is equal to :"

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"$\mathop \cup \limits_{i = 1}^{50} {X_i} =$ X₁, X₂,....., X₅₀ = 50 sets. Given each sets having 10 elements.

So total elements = 50 $\times$ 10

$\mathop \cup \limits_{i = 1}^n {Y_i} =$ $$ Y₁, Y₂,....., Y_n = n sets. Given each sets having 5 elements.

So total elements = 5 $$ \times $$ n

Now each element of set T contains exactly 20 of sets X_i.

So number of effective elements in set T = $${{50 \times 10} \over {20}}$$

Also each element of set T contains exactly 6 of sets Y_i.

So number of effective elements in set T = $${{50 \times 10} \over {20}}$

$ \therefore $${{50 \times 10} \over {20}}$=${{5 \times n} \over {20}}$

$ \Rightarrow $$ n = 30"

Let $$\mathop \cup \limits_{i = 1}^{50} {X_i} = \mathop \cup \limits_{i = 1}^n {Y_i} = T$$ where each X_i contains 10 elements and each Y_i contains 5 elements. If each element of the set T is an element of exactly 20 of sets X_i’s and exactly 6 of sets Y_i’s, then n is equal to :

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Let $$\mathop \cup \limits_{i = 1}^{50} {X_i} = \mathop \cup \limits_{i = 1}^n {Y_i} = T$$ 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 of sets Xi’s and exactly 6 of sets Yi’s, then n is equal to :

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Let $$\mathop \cup \limits_{i = 1}^{50} {X_i} = \mathop \cup \limits_{i = 1}^n {Y_i} = T$$ where each X_i contains 10 elements and each Y_i contains 5 elements. If each element of the set T is an element of exactly 20 of sets X_i’s and exactly 6 of sets Y_i’s, then n is equal to :