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 :
Numbers greater than 30000, using 22333 as digits
Given:
– Digits available: 2,2,3,3,3 (two 2’s and three 3’s)
– Number must be > 30000
– First digit must be 3
Step 1: Organize possible cases
Case 1: First two digits are 33
Remaining digits: 2,2,3
Possible arrangements:
1. 33223
2. 33232
3. 33322
Case 2: First digit 3, second digit 2
Remaining digits: 2,3,3
Possible arrangements:
4. 32233
5. 32323
6. 32332
Step 2: List all numbers in ascending order
1. 32233
2. 32323
3. 32332
4. 33223
5. 33232
6. 33322
Answer: 6 distinct numbers can be formed (Option b is correct)
