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Unformatted text preview: poker hands are there? How many have all the same suit (dont simplify these numbers). Poker hands: ( 52 5 ) . Flushes (all the same colour): ( 13 5 ) . 5. If the rst three terms of (1 + a ) n are 120+160, what are a and n ? a =4, n = 5 6. What is the coecient of x 6 y 2 in ( x + y ) 8 ? ( 8 6=28 ) 7. What is the coecient 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 Pascales Triangle is true: n r + n r + 1 = n + 1 r + 1 (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 nr You need to use part 9 in order to do it. In this case, start with the left side rst....
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 Fall '10
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 Linear Algebra, Algebra

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