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

(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?

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

x₁ + x₂ + x₃ + x₄ + x₅ = 36

3. In a class of 40 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. Eight hands go up. Then the professor asked everyone with a pierced ear to do likewise. This time there are 35 hands raised. How many students have piercings both on their ears and their noses?

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

(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?

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

x₁ + x₂ + x₃ + x₄ + x₅ = 36

3. In a class of 40 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. Eight hands go up. Then the professor asked everyone with a pierced ear to do likewise. This time there are 35 hands raised. How many students have piercings both on their ears and their noses?