Directions: Write down your solutions on paper and turn them in at the start cla

Question

Directions: Write down your solutions on paper and turn them in at the start class on the duedate shown above. Problems will be graded on correctness and of your answers in a style similar to the way exam problems will be graded. As usual, this assignment will be graded out of 20 points. At the end of the mester, your percent score on all assignments will be scaled to 15 points and this ll be the percentage score earned for the semester's written homework. rity 1. All of the students at a certain university are to be given a three letter ID code consisting of the letters A through Z with possible duplication of letters except that the third letter cannot be the same as the first letter. How many possible ID codes are there? 2. A student has 5 textbooks this semester, math, biology, chemistry, English and sociology. How many ways can she arrange them on her bookshelf if the biology book must come third? 3. A student has 15 notebooks this semester. 5 are red, 7 are blue and 3 are green. How many distinct ways can he arrange them on his bookshelf if all he cares about is color?

Explanation / Answer

1. the first letter has 26 choices from A to Z, corresponding to each of these 26 choices, the second letter also has 26 choices (since letters can repeat). hence we have total 262 choices till now. but corresponding to each of these 262 combined choice, the third letter has 25 choice (excluding the one that has already appeared in the first place, to avoid repeatition)

hence the tootal number of possible 3-letter ID codes are 262 .25 = 16900

3. the 15 notebooks can be arranged (permuted) in 15! ways out of which 5 are red, 7 are blue, 3 are green. if only color is concerned then the 5 red can arrange among themselves in 5! ways (which is same as just one arrangement), the 7 red can arrange among themselve in 7! ways and for the 3 greens, it is 3!

hence, total number of distinct ways is, 15! / (5! 7! 3!) = 360360

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