Brent@GMATPrepNow wrote:confuse mind wrote:If the 4 alphabets of TRAMPLER are picked, what is the probability that the picked up alphabets can be arranged to form TRAM?
Let's think of the 8 letters as: T, R1, A, M, P, L, E, and R2.
P(letters can spell TRAM) = (
# of outcomes where letters can spell TRAM)/(
# of ways to select 4 letters)
As always, begin with the denominator.
# of ways to select 4 letters
There 8 letters, and we must choose 4 of them.
Since order doesn't matter here, this can be accomplished in 8C4 ways.
Now the numerator.
# of outcomes where letters can spell TRAM
This can be accomplished in 2 ways:
1) T, R1, A, M
2) T, R2, A, M
So, P(letters can spell TRAM) =
2/
8C4
=
2/
70
= 1/35
Cheers,
Brent
If anyone is interested, we have a free video for calculating combinations (like 5C2) in your head. You can find it here:
https://www.gmatprepnow.com/module/gmat-counting?id=789
I approached this problem differently as elaborated below:
Given word: 8 letters (R repeated; so 7 unique letters)
1st letter can be chosen in 7 ways; probability that this letter is (T,R,A or M) = 4/7
2nd letter can be chosen in 6 ways; probability that this letter is (T,R,A or M) = 3/6
3rd letter can be chosen in 5 ways; probability that this letter is (T,R,A or M) = 2/5
4th letter can be chosen in 4 ways; probability that this letter is (T,R,A or M) = 1/4
Therefore, total probability = (4/7) * (3/6) * (2/5) * (1/4) = 1/35
