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1. In baseball, there are 24 different "base-out" configurations (ruuner out first - two outs, bases loaded - none out and so on). Suppose that a new game, sleazeball, is played where there are seven bases (excluding home plate) and each team gets five outs an inning. How many base-out configurations would be possible in sleazeball?

Where I got stuck: [WIGS] I don't about baseball very much... what does that base-out configs mean? How will I relate that to the sleazeball (which is more unfamiliar to me) and what does "where there are seven bases (excluding home plate) and each team gets five outs an inning" mean?

2. Residents of a condominium have an automatic garage door opener that has a row of 8 buttons. Each garage door has been programmed to respond to a particular set of buttons being pushed. If the condo. houses 250 families, can residents be assured that no two garage doors will open on the same signal? If so, how many additional families can be added before the eight-button code becomes inadequate? Note that the order in which the buttons are pushed is irrelevant.

[WIGS]: Is it possible that if I pushed only one of the buttons, one of the garage doors will open? Am I allowed to press a button twice or three times? I feel vague about this problem bec. that particular set of buttons is not specific in detail...

3. In international morse code, each letter in alphabet is symbolized by a series of dots and dashes. WHat is the maximum number of dots and/or dashes needed to represent any letter in the english alphabets?

[WIGS]: I know that the answer is 4. The problem is how can I show through permutations or technique in combinatorics that the answer is indeed 4?

4. Proteins are chains of molecules chosen (w/ repetition) from some 20 different amino acids. In a living cell, proteins are synthesized through the genetic code. The four key nucleotides are adenine, guanine, cytosine and uracil. Assuming A,G, C or U can appear any number of times in a nucleotide chain and that all sequences are physically possible, what is the minimum length the chains must attain to have the capability of encoding the entire set of amino acids? Note: Each sequence in the genetic code must have the same number of nucleotides.

[WIGS]: My friends told me, and I agree that the answer is 3. (Same problem as to #3)

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# Homework Help: Combinatorics (sorry for long thread)

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