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February 16th, 2014, 11:53 PM   #1
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Four-digit number

Hi,
How many four-digit number which each digit smaller than previous digit?
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February 17th, 2014, 01:04 AM   #2
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Re: Four-digit number

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February 17th, 2014, 01:21 AM   #3
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Re: Four-digit number

I don't it correct.
Because each digit smaller than previous digit
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February 17th, 2014, 01:42 AM   #4
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Re: Four-digit number

Code:
1   9876
2   9875
3   9874
4   9873
5   9872
6   9871
7   9870
8   9865
9   9864
10   9863
11   9862
12   9861
13   9860
14   9854
15   9853
16   9852
17   9851
18   9850
19   9843
20   9842
21   9841
22   9840
23   9832
24   9831
25   9830
26   9821
27   9820
28   9810
29   9765
30   9764
31   9763
32   9762
33   9761
34   9760
35   9754
36   9753
37   9752
38   9751
39   9750
40   9743
41   9742
42   9741
43   9740
44   9732
45   9731
46   9730
47   9721
48   9720
49   9710
50   9654
51   9653
52   9652
53   9651
54   9650
55   9643
56   9642
57   9641
58   9640
59   9632
60   9631
61   9630
62   9621
63   9620
64   9610
65   9543
66   9542
67   9541
68   9540
69   9532
70   9531
71   9530
72   9521
73   9520
74   9510
75   9432
76   9431
77   9430
78   9421
79   9420
80   9410
81   9321
82   9320
83   9310
84   9210
85   8765
86   8764
87   8763
88   8762
89   8761
90   8760
91   8754
92   8753
93   8752
94   8751
95   8750
96   8743
97   8742
98   8741
99   8740
100   8732
101   8731
102   8730
103   8721
104   8720
105   8710
106   8654
107   8653
108   8652
109   8651
110   8650
111   8643
112   8642
113   8641
114   8640
115   8632
116   8631
117   8630
118   8621
119   8620
120   8610
121   8543
122   8542
123   8541
124   8540
125   8532
126   8531
127   8530
128   8521
129   8520
130   8510
131   8432
132   8431
133   8430
134   8421
135   8420
136   8410
137   8321
138   8320
139   8310
140   8210
141   7654
142   7653
143   7652
144   7651
145   7650
146   7643
147   7642
148   7641
149   7640
150   7632
151   7631
152   7630
153   7621
154   7620
155   7610
156   7543
157   7542
158   7541
159   7540
160   7532
161   7531
162   7530
163   7521
164   7520
165   7510
166   7432
167   7431
168   7430
169   7421
170   7420
171   7410
172   7321
173   7320
174   7310
175   7210
176   6543
177   6542
178   6541
179   6540
180   6532
181   6531
182   6530
183   6521
184   6520
185   6510
186   6432
187   6431
188   6430
189   6421
190   6420
191   6410
192   6321
193   6320
194   6310
195   6210
196   5432
197   5431
198   5430
199   5421
200   5420
201   5410
202   5321
203   5320
204   5310
205   5210
206   4321
207   4320
208   4310
209   4210
210   3210
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February 19th, 2014, 08:37 PM   #5
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Re: Four-digit number

Quote:
Originally Posted by life24
I don't it correct.
Because each digit smaller than previous digit
If you pick 4 digits out of the possible 10, then there is only one way to arrange them so that the digits are in decreasing order. The number of possible ways to do so is 10C4 = 210, hence 210 is your answer.
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February 19th, 2014, 09:34 PM   #6
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Re: Four-digit number

Hello, life24!

Quote:
How many four-digit numbers in which each digit smaller than previous digit?







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February 20th, 2014, 04:47 AM   #7
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Re: Four-digit number

He reposted the Question here. (10 C 4 = 210 ? 120)
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February 20th, 2014, 07:16 AM   #8
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Re: Four-digit number

Hi,
The final answer is 714
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February 20th, 2014, 11:16 AM   #9
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Re: Four-digit number

Ah. So you didn't actually want the digits to be smaller than the last, just not greater. So 4444 would be allowed.
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