A lottery ticket consists of 6 integers from the set X = {1,2,...,42}. The drawi

Question

A lottery ticket consists of 6 integers from the set X = {1,2,...,42}. The drawing consists of 6 randomly drawn numbers with no repetition from X = {1,2,...,42}. Order does not matter for the ticket or the drawing! The following tickets win:

The Jackpot is all 6 matching.
Second Prize is any 5 matching.
Third Prize is any 4 matching.
Fourth Prize is any 3 matching.
Answer the following questions:
(a) How many different tickets are possible?
(b) Given a drawing, how many tickets win the Jackpot?
(c) Given a drawing, how many tickets win Second Prize?
(d) Given a drawing, how many tickets win Third Prize?
(e) Given a drawing, how many tickets win Fourth Prize?
(f) Thus, what is the total number of

Explanation / Answer

a) 42C6 = 42*41*40*39*38*37/1*2*3*4*5*6 = 5245786

b). 1

c) 6

d) 6*5/2 = 15

e) 6*5*4/3*2*1 = 20

f) 42

g) 5245744

i) 42/5245786 = 8.006 * 10-6

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