Question

how many 3-digit odd numbers greater than 600 can be created using the digits 2,3,4,5,6, and 7? repetition of digits is not allowed.

Answer 1

To create a 3-digit odd number greater than 600 using the digits 2, 3, 4, 5, 6, and 7 without repetition, there are 27 possible numbers.

Step-by-step explanation:

Case 1: If the hundreds digit is 6 or 7, then we have 4 choices for the tens digit (2, 4, 5, 7) and 3 choices for the units digit (3, 5, 7).

So, in this case, we have 4 x 3 = 12 possible numbers.

Case 2: If the hundreds digit is 5, then we have 3 choices for the tens digit (6, 4, 7) and 3 choices for the units digit (3, 7, 6).

So, in this case, we have 3 x 3 = 9 possible numbers.

Case 3: If the hundreds digit is 6, then we have 2 choices for the tens digit (4, 7) and 3 choices for the units digit (3, 5, 7).

So, in this case, we have 2 x 3 = 6 possible numbers.

Hence, the total number of 3-digit odd numbers greater than 600 that can be created is 12 + 9 + 6 = 27.