(a) How many possible functions are there if the domain consists of n points, an

Question

(a) How many possible functions are there if the domain consists of n points, and each function value takes either -1 or 1 (not both)? (b) What is the probability of having constant functions for (a) (if the domain consists of 'n' points, and each function value takes either -1 or 1 (not both))? (c) How many different seven-place license plates are possible if repetition is allowed? Assume that first three places are taken from the alphabet (total 26) and the last four places are taken from the integers {0, 1, .., 9} (total 10), e g. SSS7777 is available.

Explanation / Answer

Ans:

c)If you say there are 26 letters and 10 digits, then the result is as follows.

You have 26 choices for the first letter, 26 for the second and 26 for the third.Your have 10 choices for each of the remaining 4 positions.

So, we can have 26*26*26*10*10*10*10 different license plates.

a) there are n point,but each can have 1 or -1,so there are four combinations possible (1 to1),(1 to -1),(-1 to1),(-1 to -1).So 4 functions possible.
b)Probability of constant functions:

(1,1) and (-1 to -1) are constant functions.

Probability of constant functions=2/4=0.5

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