Question

If 3 identical prizes are available for a contest with 50 entrants. In how many ways can the prizes be distributed?

Answer 1

Can an entrant win more than 1 prize?

Answer 2

no

Answer 3

50C3

Answer 4

I need the actual number not the formula

Answer 5

\[50C3=\frac{50!}{3!(50-3)!}=you\ can\ calculate\]

Answer 6

50 choices for first prize, 49 for second, 48 for third so by counting principle it would be \(50\times 49\times 48\) but since all the prizes are identical you have to divide by the number of ways you rearrange the 3 prizes, i.e.
\[\frac{50\times 49\times 48}{3\times 2}\] cancel first, multiply last

Answer 7

Thanks guys you have been a real big help ;)