An "Error" qs from the SAT Math 1-2 book by princeton review? or I am wrong?

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1

<p>Here is the original question:</p>

<p>How many distinct 3-digit numbers contain only nonzero digits?
A) 909
B) 899
C) 789
D) 729
E) 504</p>

<p>The answer by princeton review is D) 729 (they used 9<em>9</em>9).</p>

<p>My answer is E) 504 and I used 9<em>8</em>7 because they said distinct.</p>

<p>Am I correct or my interpretation of "distinct" is wrong.</p>

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<p>youre saying the number 333 isnt distinct. i see no other 3-digit numbers like 333, so it is distinct</p>

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<p>there are 19 numbers with a 0 in the ones or tens place for each number in the hundred’s column. 9 x 19 = 171. There are 999 - 100 + 1, 3 digit numbers, or 900 3 digit numbers. That equates to 729 numbers with nonzero digits, which is 900 - 171. </p>

<p>distinct means that no two numbers have the same digits in the same order. I don’t know what you were trying to do with 9 * 8 * 7, but common sense can tell you that there’s no way there are nearly 400 numbers with a 0 in it. </p>

<p>Another way is 9C1 * 9C1 * 9C1 = 729</p>

4

<p>that’s a confusing way to put it lol…</p>

<p>whiteetea, your calculation was for how many 3 digit numbers are there with 3 distinct digits in that number. so your calculation didn’t include numbers such as 555, 696, 773, etc. in order to include those, you have 9 possibilites for the first digit, 9 for the second, and 9 for the third, multiply and fill in the bubble</p>

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<p>lol, what I written down is exactly what it is on the book.</p>

<p>Its a permutation qs.</p>

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<p>To An0maly: “distinct means that no two numbers have the same digits in the same order”. I do not really understand what u mean by that. But when they said distinct and non zero, I guess the 1st box is “9” (because zero is not counted), than 2nd Box is “8” (excluding zero and the number in the first box as they had said “distinct”) and 3rd box is “7” (excluding zero and the first and second box).</p>

<p>If they didn’t say “distinct” then I will agree with yr and the author answer which is 729.
They earlier chapter in the book defines “distinct number” as Numbers that are different from each other.</p>

7

<p>Exactly. A number that is distinct is a number that is different from another. That doesn’t mean every DIGIT IN THE NUMBER has to be different. It means the actual NUMBER is different. “Distinct” only means you can only count each number (not each digit) one time, which is pretty much a given.</p>

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<p>I posted it kinda confusion, but what I’m getting at is that your method prevents digits from repeating in the number. Like i took the sat said, it excludes the possibility of 552 and 525, although both are clearly distinct numbers.</p>

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<p>Thanks for the earlier reply (:</p>

<p>So what you’re trying to say is that 552 and 525 are distinct number?</p>

<p>But 552 and 552 are not distinct number?</p>

<p>So “distinct 3-digit numbers” laterally mean the numbers must be distinct but the digit do not need to be distinct?</p>

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<p>^exactlyyyyyyyyyyy</p>

<p>they’re asking for “distinct 3-digit numbers”</p>

<p>they’re not asking for “numbers with 3 distinct digits”</p>