Answer:
a) [tex] N= (5C1) *(5C1) *(5C1) = 5*5*5 = 125[/tex]
b) [tex] N = (5C1)*(4C1) *(3C1) = 5*4*3 = 60[/tex]
Step-by-step explanation:
For this case our sample space is the 5 letters given:
[tex] S= [F,G, H, I, J][/tex]
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:
[tex] N= (5C1) *(5C1) *(5C1) = 5*5*5 = 125[/tex]
So then we will have 125 possible combinations of 3 words letters with the 5 provided
We need to remember that [tex] nC x = \frac{n!}{(n-x)! x!}[/tex]
Part b
For this case the repetition is not allowed so then the possible number of possibilities are:
[tex] N = (5C1)*(4C1) *(3C1) = 5*4*3 = 60[/tex]
So then we will have 60 possible combinations of 3 words letters with the 5 provided
