COMBINATORIAL ANALYSIS - 8 COMPETITION QUESTIONS
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Subscribe to the channel and ask me your questions! =] ▶ Want to support the channel? =D PIX: [email protected] PDF sheet: https://drive.google.com/open?id=1P14... Combinatorial Analysis 1. In a school, the students will elect the principal, vice-principal and treasurer among the 20 teachers in the school. In how many ways can this choice be made? a) 6980 b) 6840 c) 6720 d) 6660 e) 6220 2. On a bus in Palmas, there are 7 (seven) empty seats. In how many different ways can 2 (two) people sit? a) 5 b) 14 c) 42 d) 49 3. For a trip to the museum, 8 boys and 10 girls were selected. The school's coordination thought it prudent to form a leadership committee among the selected students, with 2 boys and 3 girls being chosen. How many committees can be formed? a) A_10.3.A_8.2 b) A_10.3+A_8.2 c) C_10.3.C_8.2 d) C_10.3+C_8.2 4. A company needs a team with 6 members, three men and three women. It has 9 employees, five men and four women. Select the alternative that presents the number of different ways this team can be formed. a) 240 b) 80 c) 40 d) 60 e) 120 5. In a projection room, there are five chairs arranged in a line, side by side, and numbered from 1 to 5. Four people will occupy four of these chairs. The possible occupancies of the chairs are distinguished not only by the empty chair, but also by the arrangement of the people in the occupied chairs. In how many ways can the chairs be occupied? a) 5 b) 20 c) 24 d) 120 e) 1024 6. Given 8 lawyers and 10 doctors, how many committees containing 10 people with exactly 6 lawyers and 4 doctors can we form? a) 5880 committees. b) 5870 committees. c) 5670 committees. d) 5980 committees. e) 5480 committees. 7. Ten teams compete in a championship in which the champion and runner-up will be awarded prizes. How many classifications among the teams are possible for the first two places, assuming that there will be only one champion and one runner-up? a) 10 b) 20 c) 30 d) 50 e) 90 8. Consider the set of natural numbers {1,2, ..., 15}. Forming groups of three distinct numbers from this set, the number of groups in which the sum of the terms is odd is: a) 168 b) 196 c) 224 d) 227 e) 231
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