1. I have a new student and I have taught her 5 html tags. I give her a lab assi

Question

1. I have a new student and I have taught her 5 html tags. I give her a lab assignment in which she must use at least 20 html tags. Presuming she only uses the tags I taught her, can I be guaranteed she will use at least one tag more than once? Explain why or why not using the Pigeonhole principle.

2. I have gotten a big new office with 12 windows out onto campus. 5 pigeons fly into my office (presumably to ask me about functions). Can I be guaranteed that at least two pigeons fly through the same window to get into my office? Explain why or why not using the Pigeonhole principle.

Explanation / Answer

1) let us consider each html tag as a pigeon and each of the 20 html tags required as pigeonholes then m=5 and n=20. According to the pigeonhole principle, if n items are put into m containers, with n > m, then at least one container must contain more than one item. Since, n>m she must use the atleast one html tag that must be used more than once.

2) let us consider each of the 12 as pigeonholes then m=12 and n=5. According to the pigeonhole principle, if n items are put into m containers, with n > m, then at least one container must contain more than one item. Since, n<m therefore there are very low chances of at least two pigeons fly through the same window to get into my office.

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