[離散] HW5

[simonxander (畢玄)]

我幫自己打了一份，分享給大家

這樣就不用課本了

P.397 [6]
    Determine how many integer solutions there are to X1 + X2 + X3 + X4 = 19
    a. 0 <= Xi  i = 1~4
    b. 0 <= Xi < 8  i = 1~4
    c. 0 <= X1 <= 5, 0 <= X2 <= 6, 3 <= X3 <= 7, 3 <= X4 <= 8

P.397 [20]
    At a 12-week conference in mathematics, Sharon met seven of her friends
from college. During the conference she met each friend at lunch 35 times,
every pair of them 16 times, every trio eight times, every foursome four
times, each set of five twice, and each set of six once, but never all seven
at once. If she had lunch every day during the 84 days of the conference,
did she ever have lunch alone?

P.401 [2]
    a. In how many ways can the letters in ARRANGEMENT be arranged so that there
are exactly two pairs of consecutive identical letters? At least two pairs of
consecutive identical letters?
    b. Answer part (a), replacing two with three.

P.403 [4]
    How many permutations of 1~7 are not derangements?

P.410 [7]
    Professor Ruth has five graders to correct programs in her courses in Java,
C++, SQL, Perl, and VHDL. Graders Jeanne and Charles both dislike SQL, Sandra
wants to avoid C++ and VHDL. Paul detests Java and C++, and Todd refuses to
work in SQL and Perl. In how many ways can Professor Ruth assign each grader to
correct programs in one Language, cover all five languages, and keep everyone
content?
(You need to show the detailed computations, not only the answer.)

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