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Suppose A1, A2, ..., A30  are thirty sets each having 5 elements and B1, B2, ..., Bn  are n sets each with 3 elements, let =and each element of belongs to exactly 10 of the Ai’s and exactly 9 of the B,’S. Then n is equal to

(a) 15

(b) 3

(c) 45 

(d) 35

0 3 Views | Posted 4 months ago
Asked by Shiksha User

  • 1 Answer

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    Answered by

    Vishal Baghel | Contributor-Level 10

    4 months ago

    N u m b e r     o f     e l e m e n t s     i s     A 1 ∪ A 2 ∪ A 3 … ∪ A 3 0                                                                     = 3 0 × 5 = 1 5 0                             ( Repetition  is  not  done ) B u t     e a c h     e l e m e n t     i s     u s e d     1 0     t i m e s ∴                                                       S = 3 0 × 5 1 0 = 1 5 I f     t h e     e l e m e n t s     B 1 , B 2 , … , B n     a r e     n o t     r e p e a t e d .     T h e n     t h e     t o t a l     n u m b e r     o f     e l e m e n t s = 3 . B u t     e a c h     e l e m e n t     i s     r e p e a t e d     9     t i m e s ∴                                                       S = 3 n 9                     ⇒ 1 5 = n 3             ⇒ n = 1 5 × 3 = 4 5 H e n c e ,     t h e     c o r r e c t     o p t i o n     i s     ( c ) .

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