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In: Statistics and Probability

Code 39 is a common bar code system that consists of narrow and wide bars (black)...

Code 39 is a common bar code system that consists of narrow and wide bars (black) separated by either wide or narrow spaces (white). Each character contains nine elements (five bars and four spaces). The code for a character starts and ends with a bar (either narrow or wide) and a (white) space appears between each bar. The original specification (since revised) used exactly two wide bars and one wide space in each character. For example, if b and B denote narrow and wide (black) bars, respectively, and w and W denote narrow and wide (white) spaces, a valid character is bwBwBWbwb (the number 6). One character is held back as a start and stop delimiter.

For each of the following cases, how many characters can be encoded?

(a) The constraint of exactly two wide bars is replaced with one that requires exactly one wide bar.

(b) The constraint of exactly two wide bars is replaced with one that allows either one or two wide bars.

(c) The constraint of exactly two wide bars is dropped.

(d) The constraints of exactly two wide bars and one wide space are dropped

please help!

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