Question 127241
a) 6 ways to pick the first one in line, times 5 ways to pick the second, and so on, also expressed as {{{6!}}}.  You do the arithmetic.

b) Since you are giving 3 different prizes, the order of the outcome is significant.  Therefore, you need the Permutation of 6 things taken 3 at a time.  The formula for the Permutation of n things taken r at a time is {{{P[n,r]=n!/(n-r)!}}}. Again, you do the arithmetic.