Combinatorics

A prize draw allows you to enter by picking 3 numbers from { 1 , 2 ,..., 14 } . You will win a prize if you choose two of the three numbers that they will draw.

a) Show that it is possible to guarantee a win by having 14 entries in the draw.

b) Explain whether or not a similar strategy would work if the numbers were chosen from { 1 , 2 ,..., 21 }