Question

Harry's quidditch bag has four types of balls in it quaffles,bludgers,golden snitches and remembralls. There are 8 of each type of balls. If harry draws ball out of the bag without replacement ( he doesn't put a ball back into the bag after pulling it out),how many balls must he draws to guarantee that he has

a) at least 5 balls of the same type (explain)

b) at least 5 quaffles (explain)

Urgent please

Answer 1

a) Number of ball types = 4

Number of balls of any one type = 8

To guarantee that he has 5 balls of the same type, the worst case scenario is when he have already selected 4 balls of each of the 4 type and then picks any one of the remaining ball. That ball, whaterver type it is, will make the number of balls of that type 5.

Number of balls he must draw to guarantee 5 balls of each type = 4x4 + 1

= 17

b) To guarantee that there are at least 5 quaffles, the worst case scenario is when 4 quaffles and all non quaffles are already selected. Then there will be only quaffles remaining in the bag and whatever selection made will make number of quaffles = 5.

Number of balls he must draw to guarantee 5 quaffles = 8x3 + 4 + 1

= 29