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# 811Solutions7 - Homework 7 Solutions Kyle Chapman 137.2...

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Homework 7 Solutions Kyle Chapman November 29, 2011 137.2 This question eﬀectvely only asks how many ways are there to choose three sets of size 6 , 4 , 2. Thus the answer is ( 12 6 , 4 , 2 ) = 13860. 137.8 There are two ways to calculate this. The ﬁrst is by multiplying the odds of each number being one that was picked, which gives the result of 10 50 9 49 8 48 7 47 6 46 5 45 = . 0000132. Alternatively, we can get the result by comparing the number of ways the numbers could be picked, namely ( 50 6 ) to the number of ways that the desired numbers can be picked, which gives ( 10 6 ) . Taking the ratio of these two gives the same result. 147.2 1 We can get this rather directly from the DeMorgan’s Laws. A ( B C ) = { x | x Aorx ( B C ) } = { x | x Aor ( x Bandx C ) } = { x | ( x Aorx B ) and ( x Aorx C ) } = { x | x ( A B ) andx ( A C ) } = ( A B ) ( A C ) 2 Here we can get a simple counter example from A = B

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811Solutions7 - Homework 7 Solutions Kyle Chapman 137.2...

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