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

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25 Oct 2005, 03:45

This topic is locked. If you want to discuss this question please re-post 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:

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.

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.

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!

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.

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.

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.
_________________

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 _________________