Suppose that a tribal culture was discovered in the South Pacificwhose language

Question

Suppose that a tribal culture was discovered in the South Pacificwhose language consists of only eight letters, A,D,E,I,O,R,S, andT. Assuming that all possible arrangements of these letters couldbe words:
a) What is the maximum possible number of 5-letter words thatthis tribe can have? (I think you do this one 8x8x8x8x8? Since they canrepeat there's 8 possible letters in each of the 5 spots?)
b) What is the maximum possible number of 5-letter words thetribe can have in which no letters are repeated? (And this one would be 8x7x6x5x4? )
c) How many 8-letter words can the tribe have that start andend with an O, but contain no other O's?
d) How many 7-letter words can the tribe have that containexactly 3 E's, 2 R's, and 2 T's?
a) What is the maximum possible number of 5-letter words thatthis tribe can have? (I think you do this one 8x8x8x8x8? Since they canrepeat there's 8 possible letters in each of the 5 spots?)
b) What is the maximum possible number of 5-letter words thetribe can have in which no letters are repeated? (And this one would be 8x7x6x5x4? )
c) How many 8-letter words can the tribe have that start andend with an O, but contain no other O's?
d) How many 7-letter words can the tribe have that containexactly 3 E's, 2 R's, and 2 T's?

Explanation / Answer

a and b are correct

c)1x7x7x7x7x7x7x1

d)7!/(3!2!3!) = 70

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