Probability questions

1. There are 7 envelopes; 3 red, 2 blue, 1 green, 1 yellow. If one of the envelopes is selected at random, determine the probability that an envelope other than a blue envelope is selected?
2. CD Purchase – Neo Anderson wants to purchase six different CDs but only has enough money to purchase four. In how many ways can he select four of six CDs for purchase?
 
1. The total number of envelopes is 7. The number of envelopes other than blue is 7-2=5 envelopes. This means that the probability of selecting an envelope other than blue is
P = no. of envelopes other than blue/ total no. of envelopes = 5/7

2. By DEFINITION the number of ways in which n elements can be selected from a total of m elements is combinations (m, n) or C(m,n) (if the order of the n elements does not count) or arrangements (m,n) or A(m,n) (if the order of the n elements do count). In the text one must assume that the order of the 4 CDs does not count hence the total number is
$C(m,n) = m!/n!/(m-n)! = 6!/2!/4! = 5*6/2 = 5*3=15$ ways
(here $m! = 1*2*3*….*m$)