Question

HELP the letter tiles P, A, R, T, Y are arranged randomly. What is the probability that four tiles could be chosen randomly to spell the word TRAP

Answer 1

The question is a bit ambiguous...

If you're just making words with 4 of the 5 letters, then there is only 1 way to spell out TRAP. There are

`4!\dbinom54=(5!)/((5-4)!)=120`

ways of pulling 4 letters from the pool of 5, so the probability of spelling out TRAP is 1/120.

But if you're making words with all of the 5 letters, then there are 2 ways of having the 5 letter word contain TRAP, either YTRAP or TRAPY. There are still

`5!\dbinom55=(5!)/((5-5)!)=120`

ways of arranging the letters into a word, so the probability of this word containing TRAP is 2/120 = 1/60.