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1. How many 5 digit numerals have 9 as the first digit, 3 or 6 as the third digit, and no digit repeated?
- A. 672
- B. 672
- C. 672
- D. 672
Answer: Option A
Explanation:
Assuming decimal (base 10) numbers…
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 is 1 × 8 × 2 × 7 × 6, or 672 five-digit numbers with no digit repeated.
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