Probability (1 Viewer)

[JustRandomThings]

Hey everyone! Thanks in advance

The letters of the word PRINTER are arranged in a row. Find the probability that there are at least three letters between N and T.

I keep arriving at 4/7 but the answer says 2/7. Can anyone find flaws in my working out ty

P(at least three letters between N and T)=1-P(1 letter between N and T)-P(2 letter between N and t)
=1-(4!x2!x5x4/2!)/2520-(5!x5x2!/2!)/2520
=4/7 which is wrong

 

[InteGrand]

Hey everyone! Thanks in advance

The letters of the word PRINTER are arranged in a row. Find the probability that there are at least three letters between N and T.

I keep arriving at 4/7 but the answer says 2/7. Can anyone find flaws in my working out ty

P(at least three letters between N and T)=1-P(1 letter between N and T)-P(2 letter between N and t)
=1-(4!x2!x5x4/2!)/2520-(5!x5x2!/2!)/2520
=4/7 which is wrong

You appear to have left out the case of 0 letters between N and T.

 

[braintic]

You don't need so much combinatorics.

If you assign the positions of letters in the word numbers 1 to 7, and you don't care about the order of N and T, the number of ways of choosing the order of those letters is
7C2 = 21.

The number of ways of choosing these letters with 5 letters between them is 1 (1,7).
The number with 4 letters between is 2 (1,6 and 2,7).
With 3 letters between there are 3 possibilities (1,5 and 2,6 and 3,7).

That gives 6/21 = 2/7.