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Ms. T gave Grogg the following problem: "License plates in Mathlandia consist of six upper-case letters. For example, two possible Mathlandian license plates are ABCDEF and AAAGHE. No two license plates are the same. How many possible Mathlandian license plates are there which contain at least four s's?

Grogg got the answer $$\binom{6}{4} \cdot 26^2$$ but Ms. T told him this was the wrong answer!

(a) How did Grogg arrive at his answer?
(b) Why is Grogg's answer wrong? Should the correct answer be smaller or larger than Grogg's answer (and why)?
(c) Write a solution to Ms. T's problem, explaining in complete sentences what the correct answer to the problem should be and why.

What is the solution to Ms T's problem?

Feb 23, 2021
edited by Guest  Feb 23, 2021

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Feb 23, 2021
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Guest Feb 23, 2021
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For the community: Please don't submit solutions to this problem. This is a homework problem for an online course that does not allow students to search for answers to specific problems outside of the school.

For the original poster: We realize that homework can be challenging. If you wish to receive help from the staff or other students, we encourage you to use the resources that the online classes provide. Please don't ask or search online for homework help. We understand that it's common in today's information age to look for resources online, and in some contexts, that's a great thing! However, it's against our Honor Code. You can ask for help on the message boards, and you can learn from the official solution after you submit your answer.

(Note that the answer that people keep copying and pasting every time someone posts this problem is wrong.)

Feb 23, 2021