Download For each of the problems, use the Inclusion/Exclusion principle to

Math 113: Discrete Structures
Mckenzie West
Homework Assignment 4
Due 2/6
For each of the problems, use the Inclusion/Exclusion principle to prove your answer.
1. How many m-digit decimal sequences (using digits 0, 1, , 2 , . . . , 9) are there in which
the digits 1, 2, and 3 all appear at least once?
2. How many positive integers ≤ 630 are relatively prime to 630?
3. How many ways are there to form a committee of 10 mathematical scientists from a
group of 15 mathematicians, 12 statisticians, and 10 operations researchers with at least
one person of each different profession on the committee.
4. A wizard has five friends. During a long wizards’ conference, it met any given friend
at dinner 10 times, any given pair of friends 5 times, any given threesome of friends 3
times, any given foursome 2 times, and all five friends together only once. If in addition
it ate alone 6 times, determine how many days the wizard’s conference lasted. 1
1 Exercises
are borrowed from pp. 321-322, 331-332 of Applied combinatorics, 5th ed by Alan Tucker.
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