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t0nyt0ny
Any OA here?­­­
­
How many integers between 3000 and 4000 that have distinct digits and increase from left to right ?

(A) 20
(B) 48
(C) 60
(D) 120
(E) 600

Since the first digit is 3, all the remaining digits must be greater than 3. Hence, the three remaining digits must be chosen from the set {4, 5, 6, 7, 8, 9}. The number of ways to choose 3-number groups from these 6 is 6C3 = 20, and since only one order will be in increasing order per each group, then 20 is the final answer.

Answer: A.

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Hope it helps.­
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Bunuel Understood the combination for choosing 3 numbers but i did not understand the part where only one order wil be increasing per each group.
Can you elaborate on that using example?

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Bunuel Understood the combination for choosing 3 numbers but i did not understand the part where only one order wil be increasing per each group.
Can you elaborate on that using example?

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Sure. Consider a group such as {4, 5, 8}. There's only one way for this group to be in ascending order: 4-5-8. That's the only arrangement possible. I recommend checking similar questions for better understanding.
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Rohan271
Bunuel Understood the combination for choosing 3 numbers but i did not understand the part where only one order wil be increasing per each group.
Can you elaborate on that using example?

Posted from my mobile device
­
Sure. Consider a group such as {4, 5, 8}. There's only one way for this group to be in ascending order: 4-5-8. That's the only arrangement possible. I recommend checking similar questions for better understanding.

But in the combinations {8,7,6} is also one possibility..how do you eliminate that?
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But in the combinations {8,7,6} is also one possibility..how do you eliminate that?
­
For EACH group of 3 different numbers, there's only one way for this group to be in ascending order. For {8,7,6} it's 6-7-8, for {9,4,6} it's 4-6-9, and so on. Thus, the number of 3-number groups would match the number of 3-number groups in ascending order. Please check similar questions for better understanding.
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