MAT311 Webassign

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1. In a class of 50 students, everyone has either a pierced nose or a pierced ear. The professor asks everyone with a pierced nose to raise his or her hand. Nine hands go up. Then the professor asked everyone with a pierced ear to do likewise. This time there are 44 hands raised. How many students have piercings both on their ears and their noses?

2. The following problem refers to strings in A, B, ..., Z. How many four-letter strings are there that begin with S ?

4. Form a seven-letter word by mixing up the letters in the word COMBINE.

(a) How many ways can you do this? (b) How many ways can you do this if all the vowels have to be at the beginning? (c) How many ways can you do this if no vowel is isolated between two consonants?

5. How many solutions (using only nonnegative integers) are there to the following equation?

x1 + x2 + x3 + x4 + x5 = 36

6. How many different five-letter strings can be formed from the letters A, B, C, D, E (repeats allowed) if the first letter must be a vowel and the last letter must be a consonant?

7. Consider the following algorithm.

for i {1, 2, 3, 4, 5} do
	beep
	for j {1, 2, 3, 4} do
		beep
	for k {1, 2, 3} do
			for l {1, 2, 3, 4, 5, 6} do
				beep
			for m {1, 2, 3, 4} do
				beep

How many times does a beep statement get executed?