What is the output of the combinatorial circuit shown below? P 9 r pe (q^¬r) Opv (-q^r) O¬(p→ (q+r)) O¬(p^ (qV¬r)) D
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- The number of 5-element subsets from a set containing n elements is equal to the number of 6-element subsets from the same set. What is the value of n? (Hint: the order in which the elements for the subsets are chosen is not important.)Consider a Little League team that has 15 players on its roster. Suppose 6 of the 15 players are left-handed. How many ways are there to select 3 left-handed outfielders and have all 6 other positions occupied by right-handed players?We want to build a chatbot, so we put together a list of 10 nouns, 10 verbs, and 10 objects, so we can construct sentences of the form NOUN VERB OBJECT (e.g., "Everyone loves combinatorics"). But we notice that 3 of the words on the noun list also appear on the verb list. None of the words on the object list appear on either of the other two lists.How many sentences of the form NOUN VERB OBJECT can we make if we require that the NOUN and VERB be different words?
- Suppose 7 of the 15 players are left-handed. How many ways are there to select 3 left-handed outfielders and have all 6 other positions occupied by right-handed players?If student 10 is not selected, then student 5 should be selected how can I represent this constrain in mathematical formUse different ways to show all possible combinations in this situation
- Find the output of the combinatorial circuit. Express it with the logical operations and their notation.Suppose that there are 9 female and 12 male students in a classroom. How many different 5-member teams can be formed from only female students?Suppose a n × n chessboard is missing two opposite corners. Prove that no matter what n is,you will not be able to cover the remaining squares exactly with dominoes.
- Suppose that 10% of weightlifters use banned substances, that a weightlifter who uses banned substances tests positive for them 97% of the time, and that a weightlifter who does not use banned substances tests positive for them 5% of the time. How would I go about answering this question?In a study of pain relievers, 100people were given product A, and 74 experienced relief. In the same study, 25 people were given product B, and 16 experienced relief.Fill in the blanks below to make the most reasonable statement possible. Product ▼(Choose one: A/B) performed better in the study. That is because only % failed to get relief with this product, whereas % failed to get relief with Product ▼(Choose one:A /B).Bag A contains 10 balls of which 3 are red and 7 are blue(assume that each ball is numbered, so all balls are different from each other). Bag Y contains 10 balls of which 4 are red and 6 are blue(assume that each ball is numbered, so all balls are different from each other). In how many ways you could pick one red ball and one blue ball if one ball is picked from each of the bag?
