#
# Written by:
# -- 
# John L. Weatherwax                2009-04-21
# 
# email: wax@alum.mit.edu
# 
# Please send comments and especially bug reports to the
# above email address.
# 
#-----

# Ex 1.2: 
print( choose(9,4) )
print( choose(5,4) )
print( choose(5,1) * choose(4,3) + choose(5,2) * choose(4,2) + choose(5,3) * choose(4,1) + choose(5,4) * choose(4,0) )
print( choose(4,1) * choose(5,3) + choose(4,2) * choose(5,2) + choose(4,3) * choose(5,1) + choose(4,4) * choose(5,0) )

# Ex 1.3: 
choose(9,3) 
choose(4,1) * choose(5,2) + choose(4,2) * choose(5,1) + choose(4,3) * choose(5,0)
choose(3,1) * choose(6,2) + choose(3,2) * choose(6,1) + choose(3,3) * choose(6,0)

# Ex 1.7:
choose(7,4)

# Ex 2.4:
choose(4,3) + choose(4,2) * choose(16,1) + choose(4,1) * choose(16,2)
choose(20,3)

# Ex 2.5:
choose(5,3) + choose(5,2) * choose(20,1) + choose(5,1) * choose(20,2)
choose(25,3)

choose(5,0) * choose(20,3) + choose(5,1) * choose(20,2) + choose(5,2) * choose(20,1)

# Ex 2.6: 
sum( choose( 10, 1:6 ) * choose( 14, 6 - (1:6) ) ) / choose(24,6)
1 - choose(14,6) / choose(24,6)

1 - choose(10,6) / choose(24,6) 

no_freshman = choose(14,6) / choose(24,6)
no_sophmore = choose(10,6) / choose(24,6)
1 - no_freshman - no_sophmore

sum( choose( 10, 1:5 ) * choose( 14, 6-(1:5) ) )/choose(24,6)

# Ex 2.7:
sum( choose(9,1:6) * choose(15, 6 - (1:6) ) )/choose(24,6)

choose(17,6)/choose(24,6)

# Ex 2.8:
sum( choose( 7, 1:6 ) * choose( 11, 6 - (1:6) ) )/choose(18,6)

# Ex 2.9:
choose(19,4)/choose(20,5)

# Ex 2.10:
choose(4,1) * choose(13,5) / choose(52,5)

# Ex 2.11:
1 - choose(26,5) / choose(52,5)

choose( 4*3, 5 ) / choose(52,5)

# Ex 2.13:
#
1 - choose(10,1:10) / choose(24,1:10)
1 - choose(14,1:14) / choose(24,1:14)
1 - choose(14,2:10) / choose(24,2:10) - choose(10,2:10) / choose(24,2:10)