Algebra 2 Permutation and Combination

Question

1.      The “You-Pick-Three” Lottery gives out a first-prize for matching the three numbers drawn. How many possible tickets can match the same three numbers?

Answer 1

T = number of Tickets sold

winning Tickets will have up to 10^3 = 1,000

10 x 10 x10 winning numbers

10 possibilities for each digit: 0,1,2,3,4,5,6,7,8, or 9

if T= 1,000, there's about 1 expected winner

if T =500, there's a 50% chance of one winner

if T=10,000 there's about 10 expected winners

estimated number of winners = T/1,000

assuming the winning number has to be in order

so if 321 is a winning number, then 123, 132, 213, 231 and 312 are not winning numbers

but

actual number of winners is anywhere from zero to total Tickets sold

0 < W < T