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Number of possible combinations of alphabets

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Suppose that a tribal culture was discovered in the South Pacific whose language consists of only eight letters, A, D, E, I, O, R, S, and T. Assuming that all possible arrangements of these letters could be words:

a) What is the maximum possible number of 6-letter words that this tribe can have?
b) What is the maximum possible number of 6-letter words the tribe can have in which no letters are repeated?
c) How many 7-letter words can the tribe have that start and end with an O, but contain no other O's?
d) How many 10-letter words can the tribe have that contain exactly 5 E's, 3 R's, and 2 T's?

Suppose that in a lottery you choose 5 numbers out of 47. Five numbers are then drawn and you win a prize if you have at least 3 of the 5 numbers. What is the probability that you win something?

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Solution Summary

How to calculate the number of different words possible from a set of alphabets with repeats?

Probability of winning lottery where 5 numbers are drawn out of 47.

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Suppose that a tribal culture was discovered in the South Pacific whose language consists of only eight letters, A, D, E, I, O, R, S, and T. Assuming that all possible arrangements of these letters could be words:

a) What is the maximum possible number of 6-letter words that this tribe can have?
There are 8 letters and so maximum possible number = 8^6 where ^ means raised to the ...

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