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Case I- When 4 persons in tennis and rest in the theatre. Number of ways – = 11 C4 × 7 C7 
Case II- When 5 persons in tennis and rest in theatre number of ways= 11 C5 × 6 C6 
Case III-When 6 persons in tennis and rest in theatre= =11C6 × 5 C5 =462 Case IV-When 7 persons in tennis and rest in theatre =11C7 × 4 C4 =330 ways. Total number of ways =2(330+462) =2(792) =1584ways
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