P 16. A children's hospital in a city of about one million people is running a charity lottery called Lucky Six to raise money. Players choose six numbers from the numbers 1 to 66. The player wins if the six numbers chosen match six numbers drawn at random by the organizers. a) How many ways could the player win? b) How many ways could the player lose? c) Is this a reasonable game for the hospital to run? Explain. 17. How can the combination formula be used to determine the number of diagonals in an n-sided polygon? 18. There are 7 boys and 13 girls in the school art club. A group of 5 is needed to set up an art exhibit. How many different groups of 5 students with at least 2 boys are there to choose from? a) Solve the problem using direct reasoning. b) Solve the problem using indirect reasoning. c) Which approach do you prefer? Explain why. Closing 19. a) How are combinations and permutations similar? How are they different? Use examples in your answers. b) If you know the value of "P, how can you determine the value of "C? Use examples in your answer. Extending 20. A CD player holds five different CDs. The CD player is set on shuffle so it randomly selects songs to play from the five CDs. This chart shows the number of songs there are on each CD. CD Number Number of Songs 1 2 3 4 5 12 14 15 12 18 Determine the probability that each of the following events will happen during the first five songs played. a) The five songs will be from CD 2 and CD 4. b) One of the five songs will be from each CD. c) Your favourite song from each of the 5 CDs will be played. 21. Simplify: (3) + (2) + (") 22. Prove: +1C = Cr+nCr-1 n