Author 
Message 
Manager
Joined: 05 Oct 2005
Posts: 81

From the word TRAMPLE 4 letters are taken. What is the [#permalink]
Show Tags
25 Oct 2005, 04:45
This topic is locked. If you want to discuss this question please repost it in the respective forum.
From the word TRAMPLE 4 letters are taken. What is the probability that the word TRAM is arranged?
A. 1/2
B. 1/3
C. 1/7
D. 1/28
E. 1/35
I believe that all of these choices are incorrect. The correct answer should be 1/840.
If a word is arranged, then order matters, and we need to find the permutation instead of the combination. In this case, the probability of the word TRAM being arranged should be:
1/P(7,4)
P(7,4) = 7!/(74)! = 7!/3! = 7 x 6 x5 x 4 = 840
Thus the answer should be 1/840.
What do you guys think?



Senior Manager
Joined: 15 Apr 2005
Posts: 415
Location: India, Chennai

Re: Question Collection 1.2, #39 [#permalink]
Show Tags
25 Oct 2005, 04:51
I am no expert in Probablity. But I think 1/840 is correct.
Here is my working.
The probablity of choosing T is 1/7
The probablity of choosing R is 1/6
The probablity of choosing A is 1/5
The probablity of choosing M is 1/4
Hence (1/7)*(1/6)*(1/5)*(1/4) = 1/840



Manager
Joined: 05 Oct 2005
Posts: 81

Re: Question Collection 1.2, #39 [#permalink]
Show Tags
25 Oct 2005, 04:53
krisrini wrote: I am no expert in Probablity. But I think 1/840 is correct.
Here is my working.
The probablity of choosing T is 1/7 The probablity of choosing R is 1/6 The probablity of choosing A is 1/5 The probablity of choosing M is 1/4
Hence (1/7)*(1/6)*(1/5)*(1/4) = 1/840
I agree with you. However, the answer in the question collection takes that number and multiplies by 24 (incorrectly, in my opinion) to reach an answer of 1/35.



VP
Joined: 30 Sep 2004
Posts: 1480
Location: Germany

Re: Question Collection 1.2, #39 [#permalink]
Show Tags
25 Oct 2005, 05:29
BumblebeeMan wrote: krisrini wrote: I am no expert in Probablity. But I think 1/840 is correct.
Here is my working.
The probablity of choosing T is 1/7 The probablity of choosing R is 1/6 The probablity of choosing A is 1/5 The probablity of choosing M is 1/4
Hence (1/7)*(1/6)*(1/5)*(1/4) = 1/840 I agree with you. However, the answer in the question collection takes that number and multiplies by 24 (incorrectly, in my opinion) to reach an answer of 1/35.
but there are two steps. firstly the letters are taken out and then the letters are arranged. that means 4 letters from 7 is 7c4 is 35. then 4 letters form 4, namely RAMT, is 4c4 is 1. now the 4 letters RAMT have to be arranged so that the word TRAM comes up. there is only 1 way to do so. so its 1/35...
_________________
If your mind can conceive it and your heart can believe it, have faith that you can achieve it.



Manager
Joined: 05 Oct 2005
Posts: 81

Quote: but there are two steps. firstly the letters are taken out and then the letters are arranged. that means 4 letters from 7 is 7c4 is 35. then 4 letters form 4, namely RAMT, is 4c4 is 1. now the 4 letters RAMT have to be arranged so that the word TRAM comes up. there is only 1 way to do so. so its 1/35...
I disagree. The letters can be selected using 7c4 (which equals 35). However, you then have to multply 35 by the number of ways in which the letters can be arranged, which is 4!
35 x 4! = 840



VP
Joined: 30 Sep 2004
Posts: 1480
Location: Germany

BumblebeeMan wrote: Quote: but there are two steps. firstly the letters are taken out and then the letters are arranged. that means 4 letters from 7 is 7c4 is 35. then 4 letters form 4, namely RAMT, is 4c4 is 1. now the 4 letters RAMT have to be arranged so that the word TRAM comes up. there is only 1 way to do so. so its 1/35... I disagree. The letters can be selected using 7c4 (which equals 35). However, you then have to multply 35 by the number of ways in which the letters can be arranged, which is 4! 35 x 4! = 840
hm? you are right
_________________
If your mind can conceive it and your heart can believe it, have faith that you can achieve it.



Intern
Joined: 25 Jun 2005
Posts: 23
Location: Bay Area, CA

BumblebeeMan wrote: I disagree. The letters can be selected using 7c4 (which equals 35). However, you then have to multply 35 by the number of ways in which the letters can be arranged, which is 4!
35 x 4! = 840
There are 35 ways to select 4 letters from 7 letters. However, there is exactly one permutation of 4 letters that we are picking (TRAM) among the 4! possibilities.
So solution is 1/35.
_________________
If you can't change the people, change the people.



Senior Manager
Joined: 03 Nov 2005
Posts: 384
Location: Chicago, IL

Well, since the order the letters are chosen matters, Possible number of outcomes is 7P4=840. P=FO/EO=1/840. I thought about it this way.
_________________
Hard work is the main determinant of success



Senior Manager
Joined: 03 Nov 2005
Posts: 384
Location: Chicago, IL

dil66 wrote: BumblebeeMan wrote: I disagree. The letters can be selected using 7c4 (which equals 35). However, you then have to multply 35 by the number of ways in which the letters can be arranged, which is 4!
35 x 4! = 840 There are 35 ways to select 4 letters from 7 letters. However, there is exactly one permutation of 4 letters that we are picking (TRAM) among the 4! possibilities. So solution is 1/35.
you can't find probability (Favorable number of outcomes/ possible number of outcomes) unless you have both numerator and denominator in either combination or permutation. if order matters in the numerator, so it does in the denominator. I think
_________________
Hard work is the main determinant of success



SVP
Joined: 28 May 2005
Posts: 1707
Location: Dhaka

it should be 1/7P4 = 1/840
answer choices are not correct.
_________________
hey ya......










