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11. Find the number of functions f that map the set {1,2,3,4} into itself such that the range of the function f(x) is the same as the range of the function f(f(x).

 

12. Five girls and five boys randomly sit in ten seats that are equally spaced around a circle.  The probability that there is at least one diameter of the circle with two girls sitting on opposite ends of the diameter is m/n , where m and n are relatively prime positive integers.  Find m+n.

 

13. Five men and five women stand in a circle in random order.  The probability that every man stands next to at least one woman is m/n, where m and n are relatively prime positive integers.  Find m+n

 

14. If you roll four standard, fair six-sided dice, the top faces of the dice can show just one value (for example, 3333 ), two values (for example, 2666), three values (for example, 5215), or four values (for example, 4236).  The mean number of values that show is m/n, where m and n are relatively prime positive integers.  Find m+n.

 Jan 12, 2021
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11. There are 4^2 + 4 + 1 = 21 functions.

 

12.The probability is 4/15 ==> 4 + 15 = 19.

 

13. The probabiilty is 65/231 ==> 65 + 231 = 296

 

14. The mean value is 28/5 ==> 28 + 5 = 33.

 Jan 23, 2021

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