In a game of six digits, two digits are already fixed for prize. If any one will find these two fixed digits then he will win the prize. Mr. A selects two numbers. The probability that Mr. A will win the prize is

Options

A. `1/15`
B. `1/6`
C. `1/5`
D. `1/1`

Answer

To solve the problem, we need to determine the probability that Mr. A will win the prize by selecting the two fixed digits from a set of six digits.

### Step-by-Step Solution:

1. **Understand the Total Digits**:
There are a total of 6 digits available in the game.

2. **Identify Fixed Digits**:
Out of these 6 digits, 2 digits are fixed as the winning digits.

3. **Determine Total Ways to Select 2 Digits**:
We need to find the total number of ways to select 2 digits from the 6 available digits. This can be calculated using the combination formula:
\[ \text{Total ways to select 2 digits} = \binom{6}{2} = \frac{6!}{2!(6-2)!} = \frac{6 \times 5}{2 \times 1} = 15 \]

4. **Identify Winning Combination**:
There is only 1 way for Mr. A to select the 2 winning digits (the fixed digits).

5. **Calculate Probability**:
The probability that Mr. A will win the prize is given by the ratio of the number of winning combinations to the total combinations:
\[ \text{Probability of winning} = \frac{\text{Number of winning combinations}}{\text{Total combinations}} = \frac{1}{15} \]

### Final Answer:
Thus, the probability that Mr. A will win the prize is \(\frac{1}{15}\).

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