[離散] HW6

[roger00 (Stage Column(?))]

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有錯請指正

p.417

#2 Determine the generating function for the number of ways to distribute

   35 pennies (from an unlimited supply) among five children if

   (c) each child gets at least 2￠;(2 cents 的意思,即2 pennies)

   (e) the two youngest children must each get at least 10￠

p.431

#12 Two cases of soft drinks,24 bottles of one type and 24 of another,

    are distributed among five surveyors who are conducting taste tests.

    In how many ways can the 48 bottles be distributed so that each surveyor

    gets (a) at least two bottles of each type?

         (b) at least two bottles of one particular type and at least three

             of the other?

#16 How can Mary split up 12 hamburgers and 16 hot dogs among her sons Richard,

    Peter, Christopher, and James in such a way that James gets at least one

    hamburger and three hot dogs, and each of his brothers gets at least two

    hamburgers but at most five hot dogs?

p.435

#4  Find the generating function for the number of integer solutions of

    a) 2w + 3x + 5y + 7z = n , 0 ≦ w,x,y,z

    b) 2w + 3x + 5y + 7z = n , 0 ≦ w, 4 ≦ x,y , 5 ≦ z

p.440

#4  a) For the ship in the Example 9.28, how many signals use at least one flag

       of each color? (Solve this with an exponential generating function)

    c) How many signals are there in Example 9.28, where the total number of

       blue and black flags is even?

註: Example 9.28

    A ship carries 48 flags, 12 each of the colors red, white, blue, and black.

    Twelve of these flags are placed on a vertical pole in order to communicate

    a signal to other ships.

#10 How many 20-digit quaternary (0,1,2,3) sequences are there where:

    (a) There is at least one 2 and an odd number of 0's?

    (b) No symbol occurs exactly twice?

    (d) There are exactly two 3's or none at all?


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