दो अक्षरों के कितने सेटों के बीच उतने ही अक्षर हैं जितने कि शब्द `ARISTOCRAT` शब्द के वर्णानुक्रम में हैं -

Options

A. 2
B. 3
C. 4
D. 5

Answer

**Step-by-Step Solution:**

1. **Identify the Unique Letters in the Word "ARISTOCRAT":**
The first step is to identify the unique letters in the word "ARISTOCRAT". The letters are:
- A
- R
- I
- S
- T
- O
- C

Note that 'R' and 'T' appear twice.

2. **Count the Unique Letters:**
The unique letters in "ARISTOCRAT" are A, R, I, S, T, O, C. Thus, we have a total of 7 unique letters.

3. **Calculate the Number of Sets of Two Letters:**
To find the number of sets of two letters that can be formed from these 7 unique letters, we use the combination formula:
\[ \text{Number of combinations} = \binom{n}{r} = \frac{n!}{r!(n-r)!} \]
where \( n \) is the total number of unique letters (7) and \( r \) is the number of letters to choose (2).

So we calculate:
\[ \binom{7}{2} = \frac{7!}{2!(7-2)!} = \frac{7 \times 6}{2 \times 1} = 21 \]

4. **Conclusion:**
Therefore, the number of sets of two letters that can be formed from the unique letters of the word "ARISTOCRAT" is 21.