How many 5 digit numerals have 9 as the first digit, 3 or 6 as the third digit, and no digit repeated?

For the first digit we have exactly one choice: 9.

For the second digit we have exactly 8 choices: 0, 1, 2, 4, 5, 7, 8, and whichever of 3/6 is not used in the third digit.

For the third digit we have exactly two choices: 3 or 6.

For the fourth digit we have exactly 7 choices: 10 possibilities minus the three used in digits one, two, and three.

For the fifth digit we have exactly 6 choices: 10 possibilities minus the four used in digits one, two, three, and four.

So the number of our choices are 1 × 8 × 2 × 7 × 6, or 672 five-digit numbers with no digit repeated.