A bowl contains 10 red balls and 10 blue balls. A woman selects balls at random without looking at them. (a) How many balls must she select (minimum) to be sure of having at least three blue balls? (b) How many balls must she select (minimum) to be sure of having at least three balls of the same color? This question concerns bit strings of length six. These bit strings can be divided up into four types depending on their initial and terminal bit. Thus the types are: 0XXXX0,0XXXX1,1XXXX0,1XXXX1 How many bit strings of length six must you select before you are sure to have at least 5 that are of the same type? (Assume that when you select bit strings you always select different ones from ones you have already selected.) In a bag we have 17 balls numbered by 5+k125,k=0,,16, i.e. by 5,130,255,380,505,1755,1880,2005. If we select several balls at random, what is the smallest number of balls needed to guarantee that the selection contains at least one pair of balls that add up to 2010 ? A. 7 B. 8 C. 10 D. 11 E. 17 Draw the switch circuit diagram implementing the Boolean expression: Z=(X1+X2+X3)(Y1Y2) Here, Z represents a buzzer being controlled by 5 switches, each respectively represented by the variables X1,X2,X3,Y1 and Y2. A variable representing a switch as a value of ' 1 ' if it is "ON" (closed), and 0 otherwise. The Buzzer, Z, as a value of ' 1 ' if it's giving off the sound, and ' 0 ' otherwise. For your submission, you may either create a digital drawing of the circuit diagram, or draw the diagram on paper and upload a very clear picture of your drawing. Points will only be awarded if the drawing is legible. Convert the following binary number to decimal. Show your work using weighted sum. You can use the symbols or x for multiplication and for exponent. For example, 222 means 2 multiplied by 2 to the power of 2 . Show your work to receive full or partial credit. Convert to decimal: 101010002