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

Question

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?

krisrini · Answer

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

BumblebeeMan · Answer

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.

christoph · Answer

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...

BumblebeeMan · Answer

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

christoph · Answer

hm? you are right

dil66 · Answer

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.

rlevochkin · Answer

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.

rlevochkin · Answer

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

nakib77 · Answer

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

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

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