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