Consider reordering the letters in the word TENNESSEE. Use the technique shown in Example 9.5.11 to answer the following questions. (a) If the N's are placed first, how many ways are there to choose positions for them? 21 x If the E's are placed second, how many ways are there to choose positions for them? 5 x If the S's are placed third, how many ways are there to choose positions for them? 21 X If the T is placed fourth, how many ways are there to choose a position for it? 8 X So, the total number of ways to reorder the letters in the word TENNESSEE is 84 (b) Imagine placing the letters into positions in a different order. If the E's are placed first, how many ways are there to choose positions for them? 126 If the T is placed second, how many ways are there to choose a position for it? 8 x If the S's are placed third, how many ways are there to choose positions for them? 7 X If the N's are placed fourth, how many ways are there to choose positions for them? 6 x x. (c) When the method suggested in part (b) is used to find the total number of ways to reorder the letters in the word TENNESSEE, the result is the same as B✔ when the method of part (a) is used.

At a music festival, there are seven bands scheduled to play, numbered 1 through 7. a. How many different ways can these bands be arranged to perform? b. If band 3 is performing first and band 1 last, then how many ways can their appearances be scheduled? a. There are different ways to arrange the bands. (Simplify your answer.) b. If band 3 is performing first and band 1 last, there are different ways to arrange the bands. (Simplify your answer.) Enter your answer in each of the answer boxes.

A. How many arrangements of all letters can be made from the word COPROCESSORS

5. Find the series solution for the following wave equation: Utt - Uzz 0, 0 t, u(0, t) = u(L, t) = 0, t > 0, u(x, 0) = 6(x – ), u:(x, 0) = 0 0 < x < L, where 8(x) is the Dirac-delta function with the following property: for any continuous function f(r) in R', f(x)8(x)dr = 1.