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In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit [#permalink]
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18 Sep 2017, 19:58
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In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit number without repetition A. 12 B. 24 C. 18 D. 4 E. 28
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Re: In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit [#permalink]
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18 Sep 2017, 20:39
fitzpratik wrote: In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit number without repetition
A. 12
B. 24
C. 18
D. 4
E. 28 So Number is ABCD. Be careful how many can replace A as there is ZERO and you should get the correct answer.. A can be replaced by 2,4,7....3 ways B can be replaced by remaining 3 as one is used in place of A....3 ways C, by remaining 2 D by the left over So arrangements = 3*3*2*1=18 C
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Re: In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit [#permalink]
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18 Sep 2017, 22:11
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No of 4 digit numbers possible  4! No of 3 digit numbers possible  3! So correct 4 digit numbers is 4!  3! = 24  6 = 18
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In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit [#permalink]
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18 Sep 2017, 22:21
0 as a digit in this question makes the question interesting. Answer changes as soon as the "0" is replaced by 2 or any other digit.
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Re: In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit [#permalink]
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20 Sep 2017, 04:56
fitzpratik wrote: 0 as a digit in this question makes the question interesting.
Answer changes as soon as the "0" is replaced by 2 or any other digit. Why cant the numbers starting from 0 be considered in this scenario? I mean 0472 may be a distinct number on a code.



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In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit [#permalink]
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20 Sep 2017, 05:11



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Re: In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit [#permalink]
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20 Sep 2017, 05:15
@johneagle Bunuel is correct, each and every word of a question stem matters. If the word "number" was to be replaced by "codes" or "arrangement of 4 digits", answer would change.
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Re: In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit [#permalink]
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20 Sep 2017, 08:29
The answer is C: 18 3x3x2x1 = 18



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Re: In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit [#permalink]
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22 Sep 2017, 17:10
laddaboy wrote: No of 4 digit numbers possible  4! No of 3 digit numbers possible  3! So correct 4 digit numbers is 4!  3! = 24  6 = 18 Could you explain the thought process behind this. Why aren't you subtracting the number of 2 digits possible and number of 1 digits possible.



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Re: In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit [#permalink]
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24 Sep 2017, 18:06
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akhan126 wrote: laddaboy wrote: No of 4 digit numbers possible  4! No of 3 digit numbers possible  3! So correct 4 digit numbers is 4!  3! = 24  6 = 18 Could you explain the thought process behind this. Why aren't you subtracting the number of 2 digits possible and number of 1 digits possible. Question : In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit number without repetition We have 4 distinct digits 0,2,4,7 . The different possible 4 digit numbers are 2047,2074,2470,2407,2704,2740 4027,4072,4207,4270,4702,4720 7024,7042,7204,7240,7402,7420 I.e 18 Numbers in all. An easier way to solve this instead of writing down the numbers would be : Lets say we have 2 digits say 1,2. The number of 2 digits numbers possible is 2! ( 12,21) Lets say we have 3 digits 0,1,2. The possible number of 3 digits combinations possible is 3! ( 012,021,102,120,210,201 ) But 012 and 021 are not 3 digit numbers right ? They are 2 digit numbers ( 012 is same as 12, 021 is same as 21) Hence the correct number of 3 digit numbers possible are 3!  2 or (3!  2!) In the original question we have 4 distinct digits 0,2,4,7. The possible no of 4 digit combination is 4! , but this includes combinations such as 0247,0274 etc,... which we need to subtract from 4!. To find combinations such as 0274,0247.... we need to start the combination with 0 and the other 3 digits can be placed in any order. 0(2,4,7)  Number of ways to do this is 3! Hence the num of 4 digits number possible is 4!  3! = 18. We don't have to subtract 2 digit or 1 digit number because we are not counting them. Example : 2 digits number 24 or 47 are not part of our Initial possible set of numbers(4!) : 2047,2074,2470,2407,2704,2740 4027,4072,4207,4270,4702,4720 7024,7042,7204,7240,7402,7420 0247,0274,0427,0472,0724,0742 Hope this helps.
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In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit [#permalink]
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25 Sep 2017, 08:49
fitzpratik wrote: In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit number without repetition
A. 12
B. 24
C. 18
D. 4
E. 28 Using FCP: ____ * ____ * ____ * ____ Conditions: 1) must be a 4digit number; and 2) numbers from which to choose, no repetition: (0, 2, 4, 7) First slot can be 2, 4 or 7  there are three possibilities _ 3_ Second slot also has only three possibilities; once 2, 4, or 7 is chosen, there are three numbers left _ 3_ * _ 3_ Then, third slot, there are two numbers that remain as possibilities. Fourth slot: one possible number. _ 3_ * _ 3_ * _ 2_ * _ 1_ =\(18\) Answer C
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Re: In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit [#permalink]
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25 Sep 2017, 18:03
fitzpratik wrote: In how many ways can digits 0, 2, 4, 7 be arranged to make a 4 digit number without repetition
A. 12
B. 24
C. 18
D. 4
E. 28 Since the first digit of any number can’t be 0, there are 3 choices for the first digit. Since no digits can be repeated, the number of choices for the second, third, and fourth digits will be 3, 2, and 1, respectively. Thus, the number of ways a 4digit number can be formed is 3 x 3 x 2 x 1 = 18. Answer: C
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