Question

A box contains 48 tickets for six door prizes. Six tickets are drawn, and not replaced, to declare the winners. If serge purchases 8 tickets, determine the probability that he wins
a) the first prize
b) the first and second prizes
c) all six prizes

Answer 1

The tickets aren't replaced, so multiply the probabilities, decreasing the  denominator each time.

a) 1/48
b) (1/48)(1/47)
c) (1/48)(1/47)(1/46)(1/45)(1/44)(1/43)

Answer 2

A)$P(1st\ prize)=\frac{8}{48}$
b)$P(1st+2nd\ prizes)=\frac{8C2}{48C2}=.025$
c)$P(all\ 6\ prizes)=\frac{8C6}{48C6}=0.000002$