A board game is played with wooden pieces, where each piece shows a number on one side. There are 44 pieces altogether, and each piece shows a number from 1 to 44. (Each number from 1 to 44 is on exactly one piece.) To begin the game you randomly select 6 pieces.
How many possibilities are there for the numbers you begin with? In other words, how many different ways can you choose your 6 pieces?
Suppose that the odd numbered pieces are painted blue and the even numbered pieces are painted white. In how many ways could you select your pieces so that they are all white?
What is the probability that all the pieces you select are white? (Give your answer correct to four decimal places.)