Sophie wants to make candles to give to his friends.

It chooses a regular square bed, which has a base edge of 6 cm and a side edge of 5 cm. In a specialist shop, wax for candle is sold in 11 cm cube blocks. By melting this and pouring the molten wax into the mold, the candles are made. (When calculating, ignore the volume change during melting and casting.)

a) How many candles can Zsófi cast from a 11 cm cube block?

Zsófi wants to color the pages of the finished pyramid-shaped candles. You will color each sheet (both the system board and side panels) with one color, blue or green.

b) How many different candles can Zsófi make in this way?

(Two candles are considered different if they cannot be rotated through each other.)

Zsófi uses three different types of "magic wicks" to cast candles. Each type has a "magic wand" of white color, but when ignited (depending on the material inside), one type burns red, the other purple, and the third burns orange. On Monday, Zsófi put 6 candles in a box, two or two of each. From Tuesday every day you randomly remove a candle from the box and light it.

c) Calculate the probability that Sophie fires three different colored candles in the first three days!