In how many ways can be bowler take four wickets in a single 6 balls over?

Options

A. 6
B. 15
C. 20
D. 30

Answer

To find out how many ways a bowler can take 4 wickets in a single 6-ball over, we can use the concept of combinations. Here’s a step-by-step solution:

### Step 1: Understand the problem
We need to determine how many different ways a bowler can take 4 wickets in 6 balls. This means we are choosing 4 balls out of 6 to take wickets.

### Step 2: Use the combination formula
The number of ways to choose r items from n items is given by the combination formula:
\[ C(n, r) = \frac{n!}{r!(n - r)!} \]
In this case, n = 6 (total balls) and r = 4 (balls in which wickets are taken).

### Step 3: Substitute the values into the formula
Substituting the values into the combination formula, we have:
\[ C(6, 4) = \frac{6!}{4!(6 - 4)!} = \frac{6!}{4! \cdot 2!} \]

### Step 4: Calculate the factorials
Now, we need to calculate the factorials:
- \(6! = 6 \times 5 \times 4!\)
- \(4! = 4 \times 3 \times 2 \times 1 = 24\)
- \(2! = 2 \times 1 = 2\)

### Step 5: Substitute the factorial values back into the equation
Now we can simplify:
\[ C(6, 4) = \frac{6 \times 5 \times 4!}{4! \cdot 2} = \frac{6 \times 5}{2} \]

### Step 6: Simplify the expression
Now, simplify the expression:
\[ C(6, 4) = \frac{30}{2} = 15 \]

### Conclusion
Thus, the total number of ways a bowler can take 4 wickets in a single 6-ball over is **15**.

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