The number of ways of the letters FGHIJ can be arranged with repetition and without repetition are 125 and 60 ways respectively.
Formula for permutation with repetition
[tex]^nPr = n^r[/tex]
Formula for permutation without repetition
[tex]^nPr = \frac{n!}{n-r!}[/tex]
We have = 5
r = 3
a. If repetition is allowed,
Permutation = [tex]5^3[/tex] = 125 ways
b. If repetition is not allowed,
Permutation = [tex]\frac{5!}{5-3!}[/tex]
Permutation = [tex]\frac{5*4*3*2*1}{2*1}[/tex]
Permutation = [tex]\frac{120}{2}[/tex]
Permutation = 60 ways
Thus, the number of ways of the letters FGHIJ can be arranged with repetition and without repetition are 125 and 60 ways respectively.
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