How many 5 digit numbers are there whose digits are in increasing order?
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Math Expert Joined: 02 Sep 2009 Posts: 87568 How many positive four-digit integers have their digits in ascending
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Hide Show timer StatisticsGMAT CLUB'S CHALLENGE QUESTIONS: How many positive four-digit integers have their digits in ascending order from thousands to units? A. 6 _________________ Math Expert Joined: 02 Aug 2009 Posts: 10653
How many positive four-digit integers have their digits in ascending
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Bunuel wrote: GMAT CLUB'S CHALLENGE QUESTIONS: How many positive four-digit integers have their digits in ascending order from thousands to units? A. 6 Hi.. an easier, short and logical way.. choose 4 out of 10... there can be ONLY 1 way the 4 can be arranged in ascending order, so selection is what we are looking for and NOT arrangements.. BUT it contains numbers with 0 in thousands digit making these 3-digit numbers \(ans = 210-84=126\) D Math Expert Joined: 02 Sep 2009 Posts: 87568 Re: How many positive four-digit integers have their digits in ascending [#permalink] Bunuel wrote: GMAT CLUB'S CHALLENGE QUESTIONS: How many positive four-digit integers have their digits in ascending order from thousands to units? A. 6 Official Solution: How many positive four-digit integers have their digits in ascending order from thousands to units? A. \(6\) First of all, notice that 0 cannot be a digit of such numbers: 0 cannot be the first digit, since in this case a number will no longer be a four-digit number and become a three-digit number; and also it cannot be any other digit, since the digits must be in ascending order. So, such numbers can have only 4 different digits out of 9 (all digits but 0). The number of groups of 4 different digits out of 9 is \(9C4=126\) and since only one arrangement of any of such groups will be in ascending order then 126 is the final answer. For example, if the group of 4 we choose is {3, 5, 7, 1}, the only way to arrange this group of digits in ascending order is 1357. Answer: D Retired Moderator Joined: 25 Feb 2013 Posts: 1004 Location: India GPA: 3.82
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chetan2u wrote: Bunuel wrote: GMAT CLUB'S CHALLENGE QUESTIONS: How many positive four-digit integers have their digits in ascending order from thousands to units? A. 6 Hi.. an easier, short and logical way.. choose 4 out of 10... there can be ONLY 1 way the 4 can be arranged in ascending order, so selection is what we are looking for and NOT arrangements.. BUT it contains numbers with 0 in thousands digit making these 3-digit numbers \(ans = 210-84=126\) D Great explanation chetan2u we can reduce 1 step here because \(0\) cannot be part of any number with ascending digits so we simply need to select \(4\) digits out of \(9\) digits Hence \(9_C_4=\frac{9!}{4!5!}=126\) Current Student Joined: 18 Aug 2016 Posts: 549 Concentration: Strategy, Technology GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38
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Bunuel wrote: GMAT CLUB'S CHALLENGE QUESTIONS: How many positive four-digit integers have their digits in ascending order from thousands to units? A. 6 First Digit - A A can be 1-6 Alltogether we have 56+35+20+10+4+1 = 126 options We must try to achieve the best within us Thanks Intern Joined: 11 Apr 2014 Posts: 18 Re: How many positive four-digit integers have their digits in
ascending [#permalink] Re: A can be 1-6 Alltogether we have 56+35+20+10+4+1 = 126 options in this solution the A is not being considered for '0'... a clear and simple step would be 10c4. Please clarify why 0 is left from the numbers. Current Student Joined: 18 Aug 2016 Posts: 549 Concentration: Strategy, Technology GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38
Re: How many positive four-digit integers have their digits in ascending
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coolnaren wrote: Re: A can be
1-6 Alltogether we have 56+35+20+10+4+1 = 126 options in this solution the A is not being considered for '0'... a clear and simple step would be 10c4. Please clarify why 0 is left from the numbers. Hey coolnaren ... We must try to achieve the best within us Thanks Math Expert Joined: 02 Sep 2009 Posts: 87568 Re: How many positive four-digit integers have their digits in ascending [#permalink]
Bunuel wrote: GMAT CLUB'S CHALLENGE QUESTIONS: How many positive four-digit integers have their digits in ascending order from thousands to units? A. 6 Par of GMAT CLUB'S New Year's Quantitative Challenge Set _________________ GMAT Club Legend Joined: 03 Jun 2019 Posts: 4830 Location: India GMAT 1: 690 Q50 V34 WE:Engineering (Transportation)
Re: How many positive four-digit integers have their digits in ascending [#permalink]
Bunuel wrote: GMAT CLUB'S CHALLENGE QUESTIONS: How many positive four-digit integers have their digits in ascending order from thousands to units? A. 6 If we select 4 numbers out of 10 and deselect numbers with 0 as thousandth digit. IMO D Kinshook Chaturvedi Intern Joined: 10 Aug 2019 Posts: 16
Re: How many positive four-digit integers have their digits in ascending
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Kinshook wrote: Bunuel wrote: GMAT CLUB'S CHALLENGE QUESTIONS: How many positive four-digit integers have their digits in ascending order from thousands to units? A. 6 If we select 4 numbers out of 10 and deselect numbers with 0 as thousandth digit. IMO D Why do we take combinations? I mean the order is important right(ascending) so shouldn't it be permutation? Math Expert Joined: 02 Sep 2009 Posts: 87568 Re: How many positive four-digit integers have their digits in ascending [#permalink]
Bunuel wrote: GMAT CLUB'S CHALLENGE QUESTIONS: How many positive four-digit integers have their digits in ascending order from thousands to units? A. 6 Official Solution: First of all, notice that 0 cannot be a digit of such numbers: 0 cannot be the first digit, since in this case a number will no longer be a four-digit number and become a three-digit number; and also it cannot be any other digit, since the digits must be in ascending order. So, such numbers can have only 4 different digits out of 9 (all digits but 0). The number of groups of 4 different digits out of 9 is \(9C4=126\) and since only one arrangement of any of such groups will be in ascending order then 126 is the final answer. For example, if the group of 4 we choose is {3, 5, 7, 1}, the only way to arrange this group of digits in ascending order is 1357. Answer: D Intern Joined: 18 Apr 2020 Posts: 18 Location: Germany GPA: 4 Re: How many positive four-digit integers have their digits in ascending
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I thought of doing this question using permutation so started with filling the 1000th position and we have 9(0 can not be used at 1000th position)options for that. While doing this I realized that answer options do not have big numbers so I can easily divide by 9 and check if I find a unique answer. I divided all options by 9 and only option D passed the test. It was a shortcut to do this question. Posted from my mobile device VP Joined: 16 Jun 2021 Posts: 1072 Re: How many positive four-digit integers have their digits in ascending [#permalink]
Bunuel wrote: GMAT CLUB'S CHALLENGE QUESTIONS: How many positive four-digit integers have their digits in ascending order from thousands to units? A. 6 Total ways of chosing 4 digits = 10C4 = 210 =>210-83 = 126 Therefore IMO D Manager Joined: 01 Apr 2021 Posts: 60 Re: How many positive four-digit integers have their digits in ascending [#permalink]
Kinshook wrote: Bunuel wrote: GMAT CLUB'S CHALLENGE QUESTIONS: How many positive four-digit integers have their digits in ascending order from thousands to units? A. 6 If we select 4 numbers out of 10 and deselect numbers with 0 as thousandth digit. IMO D I don't understand this method..isn't 8765( which is in descending order) included in 10C4? Non-Human User Joined: 09 Sep 2013 Posts: 25253 Re: How many positive four-digit integers have their digits in ascending
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Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. Re: How many positive four-digit integers have their digits in ascending [#permalink] 18 Nov 2022, 08:21 Moderators: Senior Moderator - Masters Forum 3092 posts How many 5 digit decreasing numbers are there?We would now get (105)=252 decreasing five digit number.
How many 5 digit numbers are there in the number system?Q7)How many 5-digit numbers are there in all? So, 90,000 numbers are there in all.
How many five digit numbers can be formed that are the same when the order of their digits is reversed?Hence, the total possibilities of choosing a five-digit number such that it will not change after reversing its order will be the product of all the possibilities of selecting all the digits. i.e. So, the correct answer is “ 900 ”.
How many 5 digit numbers can make using 5 digits without repeating?Therefore, the number of 5-digit numbers that can be formed by using the digits 0, 1, 2,…..,7 is 5880. Hence, option D is the correct answer.
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