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A “descending number” is a threedigit number, such that the units dig [#permalink]
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15 Aug 2017, 23:33
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Re: A “descending number” is a threedigit number, such that the units dig [#permalink]
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16 Aug 2017, 00:59
[quote="Bunuel"]A “descending number” is a threedigit number, such that the units digit is less than the tens digits and the tens digit is less than the hundreds digit. What is the probability that a threedigit number chosen at random is a “descending number”? (A) 3/25 (B) 2/9 (C) 2/15 (D) 1/9 (E) 1/10 hello Bunuel how are you hope you are well!:) you know I tried to solve your questions but arrived at totally different answer the descending numbers are as follow: 210, 321, 432, 543, 654, 765, 876, 987, 320, 430, 540, 650, 760, 870, 980 total 15 numbers the total number of three digit numbers is 999100+1= 900 the probability that descending number is picked at random is 15/900 = reducing it I get 1/60 can you please say where I am wrong ? thank you !



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Re: A “descending number” is a threedigit number, such that the units dig [#permalink]
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16 Aug 2017, 01:10
dave13 wrote: Bunuel wrote: A “descending number” is a threedigit number, such that the units digit is less than the tens digits and the tens digit is less than the hundreds digit. What is the probability that a threedigit number chosen at random is a “descending number”? (A) 3/25 (B) 2/9 (C) 2/15 (D) 1/9 (E) 1/10 hello Bunuel how are you hope you are well!:) you know I tried to solve your questions but arrived at totally different answer the descending numbers are as follow: 210, 321, 432, 543, 654, 765, 876, 987, 320, 430, 540, 650, 760, 870, 980 total 15 numbers the total number of three digit numbers is 999100+1= 900 the probability that descending number is picked at random is 15/900 = reducing it I get 1/60 can you please say where I am wrong ? thank you ! you forget to consider the nos like 310 , 431,421,430,420,410,530,530,540 etc and many more that's why you came up with a wrong answer Sent from my iPhone using GMAT Club Forum mobile app



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A “descending number” is a threedigit number, such that the units dig [#permalink]
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16 Aug 2017, 01:24
Sahilpandey wrote: dave13 wrote: Bunuel wrote: A “descending number” is a threedigit number, such that the units digit is less than the tens digits and the tens digit is less than the hundreds digit. What is the probability that a threedigit number chosen at random is a “descending number”? (A) 3/25 (B) 2/9 (C) 2/15 (D) 1/9 (E) 1/10 hello Bunuel how are you hope you are well!:) you know I tried to solve your questions but arrived at totally different answer the descending numbers are as follow: 210, 321, 432, 543, 654, 765, 876, 987, 320, 430, 540, 650, 760, 870, 980 total 15 numbers the total number of three digit numbers is 999100+1= 900 the probability that descending number is picked at random is 15/900 = reducing it I get 1/60 can you please say where I am wrong ? thank you ! you forget to consider the nos like 310 , 431,421,430,420,410,530,530,540 etc and many more that's why you came up with a wrong answer Sent from my iPhone using GMAT Club Forum mobile appyou are so right, thanks! but I guess there must be a short cut to consider all such numbers, because its really time consuming... and I can`t imagine how it is doable in two minutes... there is a high risk that one number will be missing



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Re: A “descending number” is a threedigit number, such that the units dig [#permalink]
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16 Aug 2017, 01:28
Bunuel wrote: A “descending number” is a threedigit number, such that the units digit is less than the tens digits and the tens digit is less than the hundreds digit. What is the probability that a threedigit number chosen at random is a “descending number”?
(A) 3/25 (B) 2/9 (C) 2/15 (D) 1/9 (E) 1/10 From 100 to 999, there are 999  100 + 1 = 900 threedigit numbers, From 10 unit digits 0, 1, 2, ..., 9, select 3 units digits. There are totally \(10C3=\frac{10!}{3!7!}=\frac{8*9*10}{2*3}=4*3*10=120\) From each selection of 3 units digits, we could create a “descending number”. Hence, there are totally 120 “descending number”. The probability is: \(\frac{120}{900}=\frac{2}{15}\) Answer C
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Re: A “descending number” is a threedigit number, such that the units dig [#permalink]
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16 Aug 2017, 01:36
broall wrote: Bunuel wrote: A “descending number” is a threedigit number, such that the units digit is less than the tens digits and the tens digit is less than the hundreds digit. What is the probability that a threedigit number chosen at random is a “descending number”?
(A) 3/25 (B) 2/9 (C) 2/15 (D) 1/9 (E) 1/10 From 100 to 999, there are 999  100 + 1 = 900 threedigit numbers, From 10 unit digits 0, 1, 2, ..., 9, select 3 units digits. There are totally \(10C3=\frac{10!}{3!7!}=\frac{8*9*10}{2*3}=4*3*10=120\) From each selection of 3 units digits, we could create a “descending number”. Hence, there are totally 120 “descending number”. The probability is: \(\frac{120}{900}=\frac{2}{15}\) Answer C hello ! I knew it , there was a shortcut method could you please break down it in more details From 10 unit digits 0, 1, 2, ..., 9, select 3 units digits. There are totally \(10C3=\frac{10!}{3!7!}=\frac{8*9*10}{2*3}=4*3*10=120\) I have basic knowledge of combinations and permutations, but I cant understand how did you apply it here



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Re: A “descending number” is a threedigit number, such that the units dig [#permalink]
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16 Aug 2017, 01:38
In selection of 10digits, where we can choose 3 digits. Also remember in set of 3digits there is only one possible set which can be in ascending or descending order. Example for a set {1,2,3} we have 123, 132, 213, 231, 312, 321. So for descending we have a choice C(10,3) = 120
So 120/900 = 2/15
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Re: A “descending number” is a threedigit number, such that the units dig [#permalink]
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16 Aug 2017, 01:39
dave13 wrote: hello ! I knew it , there was a shortcut method could you please break down it in more details From 10 unit digits 0, 1, 2, ..., 9, select 3 units digits. There are totally \(10C3=\frac{10!}{3!7!}=\frac{8*9*10}{2*3}=4*3*10=120\) I have basic knowledge of combinations and permutations, but I cant understand how did you apply it here Cant get your ideas. Could you specify more?
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Re: A “descending number” is a threedigit number, such that the units dig [#permalink]
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16 Aug 2017, 01:41
I am sending you a direct message of the explanation
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Re: A “descending number” is a threedigit number, such that the units dig [#permalink]
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17 Aug 2017, 06:02
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Re: A “descending number” is a threedigit number, such that the units dig [#permalink]
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08 Jun 2018, 11:20
Bunuel wrote: A “descending number” is a threedigit number, such that the units digit is less than the tens digits and the tens digit is less than the hundreds digit. What is the probability that a threedigit number chosen at random is a “descending number”?
(A) 3/25
(B) 2/9
(C) 2/15
(D) 1/9
(E) 1/10 Hi My approach is  list of numbers to make a 3 digit number in descending order  9, 8, 7, 6, 5, 4, 3, 2, 1, 0 (total 10 numbers). x > y > z so x can be filled with 8 possible number because we need 2 number y and z after that. hence, total number of ways in which a descending number can be made is 8 x 2 x 1. and total number of ways to make 3 digit numbers are 10C3 (120) 8 x 2 x 1 / 120 = 16 / 120 2/15




Re: A “descending number” is a threedigit number, such that the units dig
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