Let _i=1^50X_i = _i=1^nY_i = T, where each X_i contains 10 elements and each Y_i contains …

Question

Let $\bigcup_{i=1}^{50}X_i = \bigcup_{i=1}^{n}Y_i = T$, 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 the sets $X_i$'s and exactly 6 of the sets $Y_i$'s, then $n$ is equal to:

Accepted Answer

$$\mathop  \cup \limits_{i = 1}^{50} {X_i} = $$ 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,....., Yn = 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 Xi.

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

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

So number of effective elements in set T = $${{50 \times 10} \over {20}}$$ \therefore $${{50 \times 10} \over {20}}$=${{5 \times n} \over {20}}$$

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