Question

The number of integers, greater than $7000$ that can be formed, using the digits $3,5,6,7,8$ without repetition, is

• A. 168
• B. 120
• C. 220
• D. 48

Answer 1

The Correct Option is A

The correct answer is (A) : 168
Four digit numbers greater than $7000$
$=2\times 4\times 3\times 2=48$
Five digit number $=5!=120$
Total number greater than $7000$
$=120+48=168$

Answer 2

To form numbers greater than 7000, consider two cases:  

Case 1: Four-digit numbers greater than 7000

The thousands place must be 7 or 8 (2 choices). The remaining 3 digits can be arranged in:

\[ 4 \times 3 \times 2 \text{ ways}. \]

Thus, the total number of four-digit numbers greater than 7000 is:

\[ 2 \times 4 \times 3 \times 2 = 48. \] 

Case 2: Five-digit numbers

All five-digit numbers formed using these digits are valid. The total number of arrangements for five digits is:

\[ 5! = 120. \] 

Total numbers greater than 7000:

The total number of numbers greater than 7000 is:

\[ 48 + 120 = 168. \]