Question

The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1,3,5,7,9 without repetition, is

• A. 72
• B. 120
• C. 6
• D. 12

Answer 1

The Correct Option is A

We are tasked with finding the number of four-digit numbers that satisfy the following conditions: 

• The number must be between 5000 and 10000.
• The digits must come from the set \( \{1, 3, 5, 7, 9\} \).
• No digit may be repeated.

The first digit must ensure the number is between 5000 and 10000. Therefore, it must be \( 5 \), \( 7 \), or \( 9 \). This gives us 3 choices for the first digit.

Once the first digit is chosen, there are 4 remaining digits in the set \( \{1, 3, 5, 7, 9\} \) (excluding the chosen first digit). The second digit can then be any one of these 4 digits, giving 4 choices for the second digit. For the third digit, we are left with 3 choices (the remaining digits after the first two have been selected). Similarly, for the fourth digit, there are 2 remaining choices.

The total number of valid numbers is given by the product of choices for each position:

\[ 3 \times 4 \times 3 \times 2 = 72 \]

Thus, there are 72 four-digit numbers that satisfy the given conditions.

Answer 2

The correct answer is (A) : 72
Numbers between 5000&10000 
Using digits 1,3,5,7,9