**Solutions to Practice Problems for the Lander Math Contest**

**Module 10, Solutions (29-31)**

29) The total number of “hands” is the number of combinations

52C9= 52!/(9!×43!)= 3,679,075,400.

The probability of one hand is the inverse of 52C9 =1/3,

679,075,400.

**30)** The number of ways to elect the board is equal to the

number of permutations

12P4=19,958,400.

**31)** The probability of winning the lottery is equal to:

1/(39C5)=1/575757=0.00000173684