Answer Happy

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10. 11. a) 9. Find the number of integers from 121 to 400 inclusive that are: c) a) divisible by 7. b) not divisible by 7. c) divisible by 7 and 5. d) divisible by 7 or 5. Each student is classified as a member of one of the following classes: Freshman, Sophomore, Junior, Senior. Find the minimum number of students who must be chosen in order to guarantee that at least eight belong to the same class. 12. What is the minimum number of cards that must be drawn from an ordinary deck of cards to guarantee that you have been dealt: at least three aces? Prove that in any set of 700 English words, there must be at least two that begin with the same pair of letters (in the same order), for example, STOP and STANDARD. b) at least three of at least one suit? at least three clubs?