Answer these questions based on the following information.
An electronic goods store has 3 boxes of pen drives. The capacity of each pen drive is n GB, where `n in N`.
The first box has 3 identical pen drives, each of 4 GB storage capacity, second box has 4 identical pen-drives, each of 2 GB storage capacity, and third box has 5 pen drives, each of varying or distinct storage capacities other than 2 GB and 4 GB. All the pen drives are of the same make, colour and design.
Find the number of ways of selecting any 2 distinct pen drives .

Options

A. (A) 19
B. (B) 20
C. (C) 21
D. (D) 66

Answer

To find the number of ways to select 2 distinct pen drives from the given boxes, we can follow these steps:

### Step 1: Identify the distinct pen drives
We have three boxes of pen drives:
- **Box 1**: 3 identical pen drives of 4 GB (let's denote them as A, A, A)
- **Box 2**: 4 identical pen drives of 2 GB (let's denote them as B, B, B, B)
- **Box 3**: 5 distinct pen drives of varying capacities (let's denote them as C, D, E, F, G)

From these boxes, we can identify the types of pen drives:
- Type A: 4 GB (3 identical)
- Type B: 2 GB (4 identical)
- Type C: distinct pen drives (C, D, E, F, G) (5 distinct)

### Step 2: Count the total types of pen drives
We can summarize the types of pen drives:
- A (4 GB)
- B (2 GB)
- C (distinct pen drives C, D, E, F, G)

This gives us a total of 7 distinct types of pen drives:
1. A (4 GB)
2. B (2 GB)
3. C (distinct)
4. D (distinct)
5. E (distinct)
6. F (distinct)
7. G (distinct)

### Step 3: Calculate the number of ways to select 2 distinct pen drives
To find the number of ways to select 2 distinct pen drives from these 7 types, we use the combination formula:
\[ \text{Number of ways} = \binom{n}{r} = \frac{n!}{r!(n-r)!} \]
where \( n \) is the total number of items to choose from, and \( r \) is the number of items to choose.

Here, \( n = 7 \) (the total types of pen drives) and \( r = 2 \) (the number of pen drives we want to select).

Calculating this gives:
\[ \binom{7}{2} = \frac{7!}{2!(7-2)!} = \frac{7 \times 6}{2 \times 1} = \frac{42}{2} = 21 \]

### Conclusion
Thus, the number of ways to select any 2 distinct pen drives is **21**.

---