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2. Winning the jackpot in a particular lottery requires that you select the correct three numbers...

2. Winning the jackpot in a particular lottery requires that you select the correct three numbers between 1 and 28 and, in a separate​ drawing, you must also select the correct single number between 1 and 32. Find the probability of winning the jackpot.

3. Winning the jackpot in a particular lottery requires that you select the correct five numbers between 1 and 40 and, in a separate​ drawing, you must also select the correct single number between 1 and 46. Find the probability of winning the jackpot.

The probability of winning the jackpot is ​(Type an integer or simplified​ fraction.)

4. A corporation must appoint a​ president, chief executive officer​ (CEO), chief operating officer​ (COO), and chief financial officer​ (CFO). It must also appoint a planning committee with four different members. There are 13 qualified​candidates, and officers can also serve on the committee. Complete parts​ (a) through​ (c) below.

a. How many different ways can the officers be​ appointed?

There are_different ways to appoint the officers.

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