11 people decided to spend an afternoon in two groups. A group of them decided to go to the theater and the remaining decided to play tennis. In how many ways can the group for tennis be formed? If there must be at least four people in each group?
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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