Question

How many three-letter "words" can be made from 5 different letters "FGHIJ" if...

a) repetition of letters is allowed?



b) repetition of letters is not allowed?

Answer 1

a)
`N= (5C1) *(5C1) *(5C1) = 5*5*5 = 125`

b)
`N = (5C1)*(4C1) *(3C1) = 5*4*3 = 60`

Explanation:

For this case our sample space is the 5 letters given:

`S= [F,G, H, I, J]`

And we want to find the number of three letter words can be made from the sample space with some conditions

Part a

For this case the repetition is allowed so then each time we will have 5 possibilites in order to select one letter so if we use combinatories we have:

`N= (5C1) *(5C1) *(5C1) = 5*5*5 = 125`

So then we will have 125 possible combinations of 3 words letters with the 5 provided

We need to remember that
`nC x = (n!)/((n-x)! x!)`

Part b

For this case the repetition is not allowed so then the possible number of possibilities are:

`N = (5C1)*(4C1) *(3C1) = 5*4*3 = 60`

So then we will have 60 possible combinations of 3 words letters with the 5 provided