Assignment 9 Solutions

# Assignment 9 Solutions - poker hands are there How many...

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Assignment 9: 1. Fourteen people arrive at a party. Each one shakes hands with all the people who arrived before. How many handshakes were there? There will be ( 14 2 ) handshakes since there are 14 people and every pair of people handshakes once. 2. If 10 students ask 20 questions, how many possible ways could all the questions be asked.(dont simplify) 20 questions, 10 students. There are 10 2 0 ways for the questions to be distributed, since each question has 10 possibilities. If you care about the order the questions are asked, you need another 20! multiplied by that number. 3. There are 4 countries running in a new event in the Olympics. There are 3 athletes on the podium. How many diﬀerent ways could the athletes place on the podium if each country only has one athlete or if each country has 3 athletes entered. 4 athletes, 4!/(4-3)! ways to have them on the podium. 12 athletes, 12!/(12-3)! ways to have them on the podium. 4. If there are 5 cards in a poker hand and 52 cards in a deck, how many

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Unformatted text preview: poker hands are there? How many have all the same suit (don’t simplify these numbers). Poker hands: ( 52 5 ) . Flushes (all the same colour): ( 13 5 ) . 5. If the ﬁrst three terms of (1 + a ) n are 1-20+160, what are a and n ? a =-4, n = 5 6. What is the coeﬃcient of x 6 y 2 in ( x + y ) 8 ? ( 8 6=28 ) 7. What is the coeﬃcient of x 3 in (2 x + 3) 4 ? 2 3 ( 4 1 ) = 32 8. What is the value of ( 4 ) 1 256 + ( 4 1 ) 3 64 + ( 4 2 ) 9 16 + ( 4 3 ) 27 4 + ( 4 4 ) 81 9. (2 points) Proove that the formula used to calculate Pascale’s Triangle is true: ± n r ² + ± n r + 1 ² = ± n + 1 r + 1 ² (Start with the left side and rearrange to get the right side) 10. (2 points) We want to prove the formula for the binomial theorem using induction: ( x + y ) n = n ∑ r =0 ( n r ) x r y n-r You need to use part 9 in order to do it. In this case, start with the left side ﬁrst....
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Assignment 9 Solutions - poker hands are there How many...

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