2 objects to be filled into 3 spaces

[desmond iking]

Homework Statement

The letters 'P, I, H, A, T ' are to be arranged in a row. Find the number of possible arrangement if the vocals letters occupy the even position


after filling in P, H , T into second and fourth location, now there's only 2 letter (I and A ) , to be filled into 2 locations. how to do this?

Homework Equations

The Attempt at a Solution

my ans is 3 x 2 x 3P2 = 36

 

[Ibix]

Um. My guess is that by vocals you mean vowels. In that case, it's A and I that must be in positions 2 and 4, surely?

The answer to your question depends on whether or not you are allowed multiple uses of a single letter (is PIPIP a valid sequence?). In either case, you've got two sub-series. One is the arrangement of the consonants in the odd positions; the other is the arrangement of vowels in the even positions. Since there's no crossover between the two, what is the number of combinations for each sub-series? Therefore, what is the number of combinations for the overall series?

 

[desmond iking]

Um. My guess is that by vocals you mean vowels. In that case, it's A and I that must be in positions 2 and 4, surely?

The answer to your question depends on whether or not you are allowed multiple uses of a single letter (is PIPIP a valid sequence?). In either case, you've got two sub-series. One is the arrangement of the consonants in the odd positions; the other is the arrangement of vowels in the even positions. Since there's no crossover between the two, what is the number of combinations for each sub-series? Therefore, what is the number of combinations for the overall series?

yes, A and I that must be in positions 2 and 4, surely. since position 2 and 4 are even position . am i right?

 

[Ibix]

I think so. But your first post talks about "filling in P, H , T into second and fourth location".

Do you know whether or not you are allowed to use a letter more than once?