Each set X_r contains 5 elements and each set | vedclass

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(A) Let $N$ be the total number of distinct elements in set $S$.Given that each set $X_r$ has $5$ elements and there are $24$ such sets,the total numb

Vedclass · Accepted Answer

$18$

Vedclass · Answer

(A) Let $N$ be the total number of distinct elements in set $S$.Given that each set $X_r$ has $5$ elements and there are $24$ such sets,the total number of elements counted with repetition is $5 	imes 24 = 120$.Since each element of $S$ belongs to exactly $10$ of the $X_r$'s,we have $10N = 120$,which implies $N = 12$.Similarly,each set $Y_r$ has $4$ elements and there are $n$ such sets,so the total number of elements counted with repetition is $4n$.Since each element of $S$ belongs to exactly $6$ of the $Y_r$'s,we have $6N = 4n$.Substituting $N = 12$ into the equation,we get $6(12) = 4n$.$72 = 4n$,which gives $n = 18$.

Each set $X_r$ contains $5$ elements and each set $Y_r$ contains $4$ elements and $\bigcup_{r = 1}^{24} X_r = S = \bigcup_{r = 1}^n Y_r$. If each element of set $S$ belongs to exactly $10$ of the $X_r$'s and to exactly $6$ of the $Y_r$'s,then $n$ is equal to:

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