Question

The number of numbers greater than 6000 that can be formed from the digits 3, 5, 6, 7 and 9 (no digit is repeated in a number) is equal to

• A. 264
• B. 720
• C. 192
• D. 132
• E. 544

Answer 1

The Correct Option is C

To form a number greater than 6000, the first digit must be either 6 or 7 (since the number must be greater than 6000).
Therefore, we have two choices for the first digit. Once the first digit is selected, we are left with four digits to choose from for the remaining three places.
Since no digit can be repeated, the total number of ways to arrange the remaining three digits is the product of choices for each place.
For the first digit, we have 2 choices: 6 or 7.
For the second digit, we have 4 remaining digits to choose from.
For the third digit, we have 3 remaining digits to choose from.
For the fourth digit, we have 2 remaining digits to choose from.
Thus, the total number of numbers greater than 6000 that can be formed is: \[ 2 \times 4 \times 3 \times 2 = 48 \text{ numbers for each choice of first digit.} \]
Since we have 2 choices for the first digit (6 or 7), the total number of numbers greater than 6000 is: \[ 48 \times 2 = 96 \]

The correct option is (C) : \(192\)

Answer 2

We want to find the number of numbers greater than 6000 that can be formed using the digits 3, 5, 6, 7, and 9 without repetition.

Since the numbers must be greater than 6000, they can be either 4-digit or 5-digit numbers.

Case 1: 4-digit numbers

For a 4-digit number to be greater than 6000, the first digit must be 6, 7, or 9. So, we have 3 choices for the first digit.

After choosing the first digit, we have 4 remaining digits to choose from for the second digit, 3 for the third digit, and 2 for the fourth digit.

Therefore, the number of 4-digit numbers greater than 6000 is 3 × 4 × 3 × 2 = 72.

Case 2: 5-digit numbers

Any 5-digit number formed using these digits will be greater than 6000. So, we can arrange all 5 digits in any order.

The number of 5-digit numbers that can be formed is 5! = 5 × 4 × 3 × 2 × 1 = 120.

Total number of numbers greater than 6000 is the sum of the numbers from Case 1 and Case 2:

Total = 72 + 120 = 192

Therefore, the number of numbers greater than 6000 that can be formed from the digits 3, 5, 6, 7 and 9 (no digit is repeated in a number) is equal to 192.