In how many ways can 2 doors be selected from 3 doors ?

Options

A. 1
B. 3
C. 6
D. 9

Answer

To solve the problem of selecting 2 doors from 3 doors, we can use the concept of combinations. Here’s the step-by-step solution:

### Step 1: Identify the total number of doors and the number of doors to be selected.
We have a total of 3 doors, and we need to select 2 doors from these.

### Step 2: Use the combination formula.
The number of ways to choose \( r \) items from \( n \) items is given by the combination formula:
\[ nCr = \frac{n!}{r!(n-r)!} \]
In our case, \( n = 3 \) and \( r = 2 \). Thus, we need to calculate \( 3C2 \).

### Step 3: Substitute the values into the formula.
Using the combination formula:
\[ 3C2 = \frac{3!}{2!(3-2)!} = \frac{3!}{2! \cdot 1!} \]

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

### Step 5: Plug in the factorial values.
Substituting the factorial values into the combination formula:
\[ 3C2 = \frac{6}{2 \cdot 1} = \frac{6}{2} = 3 \]

### Step 6: Conclusion.
Thus, the number of ways to select 2 doors from 3 doors is \( 3 \).

### Final Answer:
There are 3 ways to select 2 doors from 3 doors.

---