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# permutation ques

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Manager
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permutation ques [#permalink]  27 Oct 2007, 05:24
Hi Guys,

Can anyone help me in the following ques ?

Q- What is the SUM of all 3 digit numbers that can be formed using the digits 1,2 & 3 ? (repetition of digits not allowed)

(how can one calc sum)

Thanks,
JG
Senior Manager
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Re: permutation ques [#permalink]  27 Oct 2007, 06:37
greatchap wrote:
Hi Guys,

Can anyone help me in the following ques ?

Q- What is the sum of all 3 digit numbers that can be formed using the digits 1,2 & 3 ? (repetition of digits not allowed)

(how can one calc sum)

Thanks,
JG

All possible numbers out of 1,2,3 = 3! = 6 numbers
3 will appear TWICE (at unit, tenth & hundreth place) same for 2 & 1
Summation of Units place= 2X3 + 2X2 + 2X1 = 12
Summation of Tens place=1+12=13
Summation of 100th place=1+12=13

Summation = 1332
Director
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123
132
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321
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1332

just write them out and add... much faster (20 seconds) vs amit's way of 100 seconds
Senior Manager
Joined: 11 Sep 2005
Posts: 329
Followers: 1

Kudos [?]: 54 [0], given: 0

123
132
213
231
312
321
-----
1332

just write them out and add... much faster (20 seconds) vs amit's way of 100 seconds

Hahaha.....good one

Dude now let's extend this challenge...........instead of 1,2,3 do it for 1,2,3,4,5..........i suppose on GMAT we can expect a little trickier than 1,2,3......... .........now what????? Tell me???? i'm rite here
VP
Joined: 08 Jun 2005
Posts: 1146
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singh_amit19 wrote:
123
132
213
231
312
321
-----
1332

just write them out and add... much faster (20 seconds) vs amit's way of 100 seconds

Hahaha.....good one

Dude now let's extend this challenge...........instead of 1,2,3 do it for 1,2,3,4,5..........i suppose on GMAT we can expect a little trickier than 1,2,3......... .........now what????? Tell me???? i'm rite here

singh_amit19

1,2,3,4,5

n = 5! = 120

120/5 = 24

24*1 = 24
24*2 = 48
24*3 = 72
24*4 = 96
24*5 = 120

total = 360

360000+36000+3600+360+36 = 399,996

Manager
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kool [#permalink]  27 Oct 2007, 20:44
Thanks a lot guys for the solution.

I came across a similar ques. can anyone explain this one.

Q- How many number of times will the digit 3 be written when listing integers from 1 to 1000?
Manager
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I learned, and had to relearn how to do your final question.

how many times does 3 appear in 1-1000?
number of times 3 appears all 3 times: 333 = 3
number of times 3 appears as 2 digits:
33x, 3x3, xx3
Probablities of each digit space for 33x are:
(1)(1)(9)=9, multiply by 3 to get the three different digit sets = 27 numbers that have three, but three appears twice each set, so 27*2=54 3's.
number of times 3 appears as 1 digit:
3xx, x3x, xx3
Probabilities:(1)(9)(9)=81, times three for the three sets = 243 (don't multiply this again because 3 appeared on once each set)
so, 243+3+54=300

Hope that helps.
Manager
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kool...thx [#permalink]  29 Oct 2007, 03:52
[quote="ben928"]I learned, and had to relearn how to do your final question.

how many times does 3 appear in 1-1000?
number of times 3 appears all 3 times: 333 = 3
number of times 3 appears as 2 digits:
33x, 3x3, xx3
Probablities of each digit space for 33x are:
(1)(1)(9)=9, multiply by 3 to get the three different digit sets = 27 numbers that have three, but three appears twice each set, so 27*2=54 3's.
number of times 3 appears as 1 digit:
3xx, x3x, xx3
Probabilities:(1)(9)(9)=81, times three for the three sets = 243 (don't multiply this again because 3 appeared on once each set)
so, 243+3+54=300

Hope that helps.[/quote]

Hey, [b]thanks[/b] for the explaination...I understood the logic. Man does these type of ques really come.
Manager
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new ques [#permalink]  29 Oct 2007, 04:03
this new question confused me ...

Q- How many numbers greater than 0 and less than one million can be formed with the digits 0,7,8 ?
Intern
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singh_amit19

1,2,3,4,5 ~ abcde

n = 5! = 120

120/5 = 24 ~ [color=red]Does it mean for each place (ie: a,b,c,d,e) each digit appear 24 times?[/color]
24*1 = 24
24*2 = 48
24*3 = 72
24*4 = 96
24*5 = 120

total = 360

360000+36000+3600+360+36 = 399,996 ~ [color=red]why was it 36 + 360+3600... Why didnt it start with 360 as you caculated total above?[/color]

[/quote]

This is such an interesting way!! I didnt quite understand your caculation. Please kindly help explain !
Manager
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difference [#permalink]  03 Nov 2007, 07:11
Can anyone tell me the difference between the two ques:

Q-1 How many six letter words can be formed by re-arranging the letters of the word 'NATIVE' begining with 'N' and ending with 'E'.

A- here we did 4P4. or 4! as the two words r fixed.
If they were not fixed we would have multiplied by 2!. OK.

Q-2 In how many ways can the letters of the word 'DOUBLE' be re-arranged such that the order in which the vowels appear in the word does not change.

A- Here shouldnt it be _OU_ _ E. so OUE fixed. so why isnt anwer 3!. or if its isnt fixed why isnt answer 3! * 3! .

Thanks,
VP
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Re: difference [#permalink]  03 Nov 2007, 07:20
greatchap wrote:
Can anyone tell me the difference between the two ques:

Q-1 How many six letter words can be formed by re-arranging the letters of the word 'NATIVE' begining with 'N' and ending with 'E'.

A- here we did 4P4. or 4! as the two words r fixed.
If they were not fixed we would have multiplied by 2!. OK.

Q-2 In how many ways can the letters of the word 'DOUBLE' be re-arranged such that the order in which the vowels appear in the word does not change.

A- Here shouldnt it be _OU_ _ E. so OUE fixed. so why isnt anwer 3!. or if its isnt fixed why isnt answer 3! * 3! .

Thanks,

How many six letter words can be formed by re-arranging the letters of the word 'NATIVE' begining with 'N' and ending with 'E'.

Since N and E are constant then you are asking about rearranging four letters ---> 4!

In how many ways can the letters of the word 'DOUBLE' be re-arranged such that the order in which the vowels appear in the word does not change.

Same solution here you need to rearrange three letters ---> 3! ---> but you can also move some vowels around (i.e _OU_ _ E or OU_ _ E_ or OU__ _ E) just as long you keep them in the original order.

VP
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alohagirl wrote:
KillerSquirrel wrote:
singh_amit19 wrote:

singh_amit19

1,2,3,4,5 ~ abcde

n = 5! = 120

120/5 = 24 ~ Does it mean for each place (ie: a,b,c,d,e) each digit appear 24 times?

24*1 = 24
24*2 = 48
24*3 = 72
24*4 = 96
24*5 = 120

total = 360

360000+36000+3600+360+36 = 399,996 ~ why was it 36 + 360+3600... Why didnt it start with 360 as you caculated total above?

This is such an interesting way!! I didnt quite understand your caculation. Please kindly help explain !

the logic is simple:

What is the sum of all 3 digit numbers that can be formed using the digits 1,2 & 3 ? (repetition of digits not allowed).

To find all the 3 digit numbers we apply 3! = 6

123
132
213
231
321
312

1*2 = 2
2*2 = 4
3*2 = 6

total = 12

12*100+12*10+12*1 = 1332 ---> I started with 12*100 since we had three digit numbers (i.e. base 100)

you can apply the same logic for five digit as well.

CEO
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Re: permutation ques [#permalink]  03 Nov 2007, 08:03
greatchap wrote:
Hi Guys,

Can anyone help me in the following ques ?

Q- What is the sum of all 3 digit numbers that can be formed using the digits 1,2 & 3 ? (repetition of digits not allowed)

(how can one calc sum)

Thanks,
JG

3! ways to arrange the digist w/ no repitition.

123
132
231
213
321
312

1332
Manager
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Re: [#permalink]  07 Mar 2008, 04:13
KillerSquirrel wrote:
alohagirl wrote:
KillerSquirrel wrote:

singh_amit19

1,2,3,4,5 ~ abcde

n = 5! = 120

120/5 = 24 ~ Does it mean for each place (ie: a,b,c,d,e) each digit appear 24 times?

24*1 = 24
24*2 = 48
24*3 = 72
24*4 = 96
24*5 = 120

total = 360

360000+36000+3600+360+36 = 399,996 ~ why was it 36 + 360+3600... Why didnt it start with 360 as you caculated total above?

hey if we apply the same logic for numbers 1,2,3,4 & 5 as mentioned above then wont the answer be - 3999960

24*1 = 24
24*2 = 48
24*3 = 72
24*4 = 96
24*5 = 120

total = 360

So 360 + 360*10 + 360*100 + 360*1000 + 360* 10000
=> 360 + 3600 + 36000 + 360000 + 3600000
= 3999960

AM I right ?
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Re: [#permalink]  07 Mar 2008, 07:31
123
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213
231
312
321
-----
1332

just write them out and add... much faster (20 seconds) vs amit's way of 100 seconds

yea, theres only 3! = 6 sets to write out. would be very quick.
_________________

You tried your best and you failed miserably. The lesson is 'never try'. -Homer Simpson

Manager
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Re: permutation ques [#permalink]  07 Mar 2008, 08:18
Permutation & Combination is a topic which has always bothered me.

Here are 3 ques which I am unable to solve.

Q-1 A committe of 2 hawkers and 3 shopkeepers is to be formed from 7 hawkers and 10 shopkeepers. Find the number of ways in which this can be done if a particular shopkeeper is included and a particular hawker is excluded ?

(a) 120 (b) 240 (c) 540 (d) 720 (e) 2520

Q-2 In how many ways can a committe of 5 persons be formed out of 6 men and 4 women when at least one women has to be necessarily selected ?

(a) 6 (b) 252 (c) 246 (d) 251 (e) None of these

Q-3 During a tournament, each of the ten members of a certain chess club plays every other member exactly three times. How many games occur during the tournament ?

(a) 3^10 (b) 10^3 (c) 1200 (d) 135 (e) 720

[The ques below was solved by me but I have a query]
Q-X Everyone shakes hand with everyone. If there are 66 handshakes whats the total number of people.

(a) 11 (b) 12 (c) 13 (d) 14 (e) 15

Answer is : 12.. I did it. What I did was put values one by one. Like 11C2 or 12C2 and see if its 66 or not.

But what I wanna ask is why we do 12C2. I mean why C2. Whats the importance of 2 here.

Can anyone provide explanations as well. Please. Thanks a lot.
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Re: permutation ques [#permalink]  07 Mar 2008, 09:39
A committee of 2 hawkers and 3 shopkeepers is to be formed from 7 hawkers and 10 shopkeepers. Find the number of ways in which this can be done if a particular shopkeeper is included and a particular hawker is excluded?

This problem was a bit messy because you have to be sure of what exacly you are doing. Took me about 3 minutes to clean up my own thoughts.

7 hawkers
Exclude 1 --> 6 hawkers
6C2 = 15

10 shopkeepers
If we include one in the group of 3, we only have to choose 2 to be in the group of 3.
We have to account for the one that we already included. 10 - 1
9C2 = 36

15*36 = 540
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You tried your best and you failed miserably. The lesson is 'never try'. -Homer Simpson

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Re: permutation ques [#permalink]  07 Mar 2008, 09:47
In how many ways can a committee of 5 persons be formed out of 6 men and 4 women when at least one women has to be necessarily selected ?
At least one = Total - none

Total
10C5 = 252

None
6C5 = 6

252-6 = 246
_________________

You tried your best and you failed miserably. The lesson is 'never try'. -Homer Simpson

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Re: permutation ques [#permalink]  07 Mar 2008, 09:50
During a tournament, each of the ten members of a certain chess club plays every other member exactly three times. How many games occur during the tournament ?

plays each other = 10C2
plays each other twice = 2* 10C2
plays each other 50 times = 50 *10c2

plays each other 3 times = 3 *10C2 = 135
_________________

You tried your best and you failed miserably. The lesson is 'never try'. -Homer Simpson

Re: permutation ques   [#permalink] 07 Mar 2008, 09:50

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