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A shipment of 25 television sets contains three defective units. In how many ways can a vending company purchase four of these units and receive (a) all good units, (b) two good units, and (c) at least two good units?

You are dealt five cards from an ordinary deck of \( 52 \) playing cards. In how many ways can you get (a) a full house and (b) a five-card combination containing two jacks and three aces? (A full house consists of three of one kind and two of another. For example, \( A-A-A-5-5 and K-K-K-10-10 \) are full houses.)

You and a friend agree to meet at your favorite fast - food restaurant between \( 5:00 \) and \( 6:00 \) P.M.The one who arrives first will wait \( 15 \) minutes for the other, and then will leave (see figure). What is the probability that the two of you will actually meet,assuming that your arrival times are random within the hour?

A clothing manufacturer interviews \( 12 \) people for four openings in the human resources department of the company. Five of the \( 12 \) people are women. If all \( 12 \) are qualified, in how many ways can the employer fill the four positions if (a) the selection is random and (b) exactly two women are selected?

In Exercises 67 - 72, expand the expression in the difference quotient and simplify. \( \dfrac{f\left(x + h\right) - f\left(x\right)}{h} \quad \quad \) Difference quotient \( f(x) = \sqrt{x} \)

A police department uses computer imaging to create digital photographs of alleged perpetrators from eyewitness accounts. One software package contains \( 195 \) hairlines, \( 99 \) sets of eyes and eyebrows, \( 89 \) noses, \( 105 \) mouths, and \( 74 \) chins and cheek structures. (a) Find the possible number of different faces that the software could create. (b) An eyewitness can clearly recall the hairline and eyes and eyebrows of a suspect. How many different faces can be produced with this information?

In Exercises 71-76, write the first five terms of the sequence. (Assume that \( n \) begins with 0.) \( a_n = \dfrac{1}{(n + 1)!} \)

A weather forecast indicates that the probability of rain is \( 40\% \). What does this mean?

In Exercises 73 - 76, find the number of diagonals of the polygon. (A line segment connecting any two non adjacent vertices is called a diagonal of the polygon.) Decagon (\( 10 \) sides)

Toss two coins 100 times and write down the number of heads that occur on each toss (0, 1, or 2). How many times did two heads occur? How many times would you expect two heads to occur if you did the experiment 1000 times?