A basket ball team consists of 12 pairs of twin brothers. On the first day of training, all 24 players stand in a circle in such a way that all pairs of twin brothers are neighbours. Number of ways this can be done is :

Options

A. ` (12)!2^(11) `
B. ` (11)!2^(12) `
C. ` (12)!2^(12) `
D. ` (11)!2^(11) `

Answer

To solve the problem of arranging 12 pairs of twin brothers in a circle such that each pair stands next to each other, we can follow these steps:

### Step 1: Treat Each Pair as a Single Unit
Since each pair of twin brothers must stand next to each other, we can treat each pair as a single unit or block. Therefore, instead of arranging 24 individual players, we will arrange 12 blocks (pairs).

### Step 2: Arrange the Pairs in a Circle
When arranging \( n \) objects in a circle, the number of arrangements is given by \( (n-1)! \). Here, we have 12 pairs (blocks), so the number of ways to arrange these pairs in a circle is:
\[ (12 - 1)! = 11! \]

### Step 3: Arrange the Twins Within Each Pair
Each pair consists of 2 twin brothers, and they can be arranged in 2 ways (since they are indistinguishable). Therefore, for each of the 12 pairs, we can arrange the twins in:
\[ 2! = 2 \text{ ways} \]
Since there are 12 pairs, the total arrangements for the twins within all pairs is:
\[ 2^{12} \]

### Step 4: Combine the Arrangements
To find the total number of arrangements, we multiply the number of ways to arrange the pairs in a circle by the number of ways to arrange the twins within each pair:
\[ \text{Total arrangements} = 11! \times 2^{12} \]

### Final Answer
Thus, the total number of ways the basketball team can stand in a circle with each pair of twin brothers as neighbors is:
\[ 11! \times 2^{12} \]