1 Press Ctrl-A ©G Dear2009 – Not to be sold/Free to use Probability & Counting Stage 6 - Year 12 General Mathematic (HSC)

2 Probability & Counting Techniques number of arrangements Once we know the number of arrangements O, C, T, U, N The letters O, C, T, U, N are written on cards. COUNT What is the probability of the letters forming COUNT ? Total Number of Arrangements = 5!= 120 COUNT P(COUNT) = End of Slide ordered and the number of ordered unordered selections or unordered selections probabilities we can work out the probabilities.

3 John, Mary, Helen, Peter and Bob are in a race. first two What is the probability of Helen and Peter being in the first two places? Total Number of Ordered Arrangements = = 20 5 x 4 Helen & Peter P(Helen & Peter) = 2 20 Number of Arrangements Helen & Peter = 2!= 2 = 1 10 Probability & Counting Techniques End of Slide

4 redblueorange A bag contains a red, green, white, blue, orange marbles. redblue What is the probability of the red, white and blue marbles being chosen. Total Number of Ordered Arrangements = = 60 5 x 4 x 3 R,W,B) P(R,W,B) = 6 60 Number of Arrangements of Colours = 3!= 6 = 1 10 Probability & Counting Techniques End of Show