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1answer
36 views

How many strings are there (inclusion exclusion principle)

Q: What is the number of strings with the length of $8$ above $\left\{1,2,\cdots,10\right\}$ where $7,8$ appears at least one time? So by using the inclusion exclusion principle: $10^8$ ...
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3answers
412 views

Prove: Number of Derangement is odd if and only if number of items is even .

let $D_n$ be a number of Derangement of n items . prove that $D_n$ is odd if and only if n is even . i was trying to use induction on the $!n=(n-1)(!(n-1)+!(n-2))$ recurrence relation but i cant ...
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0answers
201 views

discrete math party question

I have a discrete math question here but im not sure how to approach it with inclusion-exclusion. Can someone help me out? Consider a party of 60 persons. Assume that each person knows more than m ...