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Test 3 Solutions

# Test 3 Solutions - F06/CS 191 Suggested Solutions to TEST...

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F06/CS 191 : Suggested Solutions to TEST THREE Discrete Structures I 12/12/2006, 5:45-7:45pm OPEN BOOK Name_____________________ There are 5 problems with 20 points each0 plus a makeup problem for the second test. 1 (a) Convert the following decimal number into a hexadecimal number and then a binary  number: 6591   Solution: 6591 = (19BF) 16  = (1 1001 1011 1111)  2 ( b ) Convert the following hexadecimal decimal number into a decimal number: 3DAB Solution: 3DAB = 3   (16) 3  + 13   (16)  2  + 10   (16) + 11 1

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= 3   4096 + 13   256 + 10   16 + 11  = 12288 + 3328 + 160 + 11 = 15787. 2 Five women and ten men are on the faculty in the mathematics department at a  school. (a)   How   many   ways   are   there   to   select   a   committee   of   four   members   of   the  department if at least one woman must be on the committee? Please give the  formula and its value. Solution: Let X = {a committee of four persons with no restriction} Y = {a committee of four men only} Then, the answer is |X| – |Y|.
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