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# the digits 5,6,7,8 can be arranged without repetition to form the no.

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Intern
Joined: 05 Feb 2014
Posts: 3
the digits 5,6,7,8 can be arranged without repetition to form the no.  [#permalink]

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17 Feb 2017, 20:53
2
The digits 5,6,7,8 can be arranged without repetition to form the no. 7685. According to the given data,find the position of 7685 if the 4-digit numbers formed using the given digits are arranged from the start in ascending order and from the end in descending order of magnitude?

Answer: Position of 7685 from start in ascending order = 16
Position of 7685 from end in descending order=9
Math Expert
Joined: 02 Aug 2009
Posts: 7213
Re: the digits 5,6,7,8 can be arranged without repetition to form the no.  [#permalink]

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17 Feb 2017, 22:22
30061989 wrote:
The digits 5,6,7,8 can be arranged without repetition to form the no. 7685. According to the given data,find the position of 7685 if the 4-digit numbers formed using the given digits are arranged from the start in ascending order and from the end in descending order of magnitude?

Answer: Position of 7685 from start in ascending order = 16
Position of 7685 from end in descending order=9

Hi...
1) in ascending order..
Before the thousands digit becomes 7, it can take 5 and 6..
a) With 5 in thousands digit, 5_ _ _, rest three digits 6,7 and 8 can be arranged in 3!=6 ways..
b) Similarly with 6 as thousands digit, 6 _ _ _, 3! Or 6 numbers can be formed..
c) Now with 7 as thousands digit, 5 can be in hundreds digit, 75_ _and remaining 2 in 2! Ways..
With 7 in thousands, and 6 in hundreds.....7658 is one possibility
After that is the number required 7685..

So the position is 6+6+2+1+1=16..

2) in descending order..
Total all ways 4!=24..
So if 16 in ascending order, 24-16+1 in descending order..
Ans 9

OR..
We can find in the similar way as (1) above

Hope it helps
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Intern
Joined: 05 Feb 2014
Posts: 3
the digits 5,6,7,8 can be arranged without repetition to form the no.  [#permalink]

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18 Feb 2017, 02:14
I understood the 1st part but the 2nd part went over my head. Why did you add "1" at last.
Total no. of ways in which 4 digits can be arranged= 4!=24
from the 1st part: position in ascending order=16
But why the "1" at last?

For the 2nd part: In the question,it's given that the digits are arranged FROM THE END in DESCENDING ORDER.
If the question would have given "arranged from the start in descending order",then I can solve it but the question says something different.

Plz explain!
Math Expert
Joined: 02 Aug 2009
Posts: 7213
: the digits 5,6,7,8 can be arranged without repetition to  [#permalink]

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18 Feb 2017, 05:43
30061989 wrote:
I understood the 1st part but the 2nd part went over my head. Why did you add "1" at last.
Total no. of ways in which 4 digits can be arranged= 4!=24
from the 1st part: position in ascending order=16
But why the "1" at last?

For the 2nd part: In the question,it's given that the digits are arranged FROM THE END in DESCENDING ORDER.
If the question would have given "arranged from the start in descending order",then I can solve it but the question says something different.

Plz explain!

Hi...
When you subtract two numbers, you get the difference but not the POSITION..
Let's take a smaller set ..

Say there are 5 numbers in ascending order.. 1,2,3,4,5
What is 4 from end..
If you take 5-4, you get 1, but FIRST will be 5 and 4 will be SECOND..
That is why we add ONE........ 5-4+1=2..
So 4 is 2nd in descending order..

Hope it helps
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

: the digits 5,6,7,8 can be arranged without repetition to &nbs [#permalink] 18 Feb 2017, 05:43
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# the digits 5,6,7,8 can be arranged without repetition to form the no.

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