# Q. Using 2, 2, 3, 3, 3 as digits, how many distinct numbers greater than 30000 can be formed?

(a) 3

(b) 6

(c) 9

(d) 12

Correct Answer: (b) 6

#### Question from UPSC Prelims 2021 CSAT Paper

**Explanation : **

## Number Formation Analysis – Greater than 30000

Since the number must be greater than 30000, the first digit must be 3. This leaves us with four digits: 2, 2, 3, and 3.

There are two cases to consider:

- The second digit is also a 3. In this case, we have three digits left: 2, 2, and 3. There are three ways to arrange these digits (223, 232, and 322), so there are three numbers that can be formed in this case.
- The second digit is a 2. In this case, we have three digits left: 2, 3, and 3. There are also three ways to arrange these digits (233, 323, and 332), so there are three numbers that can be formed in this case.

In total, there are 6 distinct numbers greater than 30000 that can be formed using the given digits.