Question

In a cricket team if the number of ways in which we can arrange n Bowlers and n Batsmen at a round table so that neither any 2 Bowlers nor 2 Batsmen sit next to one another is 2880. Then the value of n equals to

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

Answer: (C)

5

Answer 2

To ensure that no two bowlers sit together and no two batsmen sit together around a round table, the arrangement must be alternating (e.g., B A B A ...).

1. Arrange the $n$ distinct bowlers around the round table. The number of ways to do this is $(n-1)!$.
2. This creates $n$ spaces between the bowlers. The $n$ distinct batsmen must occupy these spaces. The number of ways to arrange $n$ batsmen in $n$ spaces is $n!$. The total number of arrangements is the product: $(n-1)! \times n!$. We are given that this equals 2880. $(n-1)! \times n! = 2880$. Testing values: For $n=3$, $2! \times 3! = 2 \times 6 = 12$. For $n=4$, $3! \times 4! = 6 \times 24 = 144$. For $n=5$, $4! \times 5! = 24 \times 120 = 2880$. Thus, $n=5$.