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# From the word TRAMPLE 4 letters are taken. What is the

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Manager
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From the word TRAMPLE 4 letters are taken. What is the [#permalink]  25 Oct 2005, 03:45
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!/(7-4)! = 7!/3! = 7 x 6 x5 x 4 = 840

Thus the answer should be 1/840.

What do you guys think?
Senior Manager
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Re: Question Collection 1.2, #39 [#permalink]  25 Oct 2005, 03:51
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
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Re: Question Collection 1.2, #39 [#permalink]  25 Oct 2005, 03:53
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.
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Re: Question Collection 1.2, #39 [#permalink]  25 Oct 2005, 04:29
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...
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Manager
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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
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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
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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.
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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.
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Senior Manager
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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
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it should be 1/7P4 = 1/840

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hey ya......

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