1. a box containing 6 red balls and 4 green balls. how many ways can 2 balls be drawn at the time if
a. the balls are of any color?

The number of ways to choose 2 from 10 balls, C(10,2) = 45


b. in the balls are of the same color?

The number of ways to choose 2 red balls from 6 red balls, C(6,2) = 15 +
The number of ways to choose 2 green balls from 4 green balls, C(4,2) = 2.
Answer 15+2=17. 



c. if the two balls are different color?

For each of the 6 ways to choose the red ball, there are 4 ways
to choose the green ball.  So that 6*4 or 24


2. a sample of 12 students will be taken from a class with 26 girls and 15 boys. In how many ways can a sample be taken if
a. there must be equal number of boys and girls

For each of the C(26,6) ways to choose the 6 girls from the 26, there are
C(15,6) ways to choose the 6 boys from the 15.  Thats C(26,6)*C(15,6)
or 1152301150


b. gender is not a consideration

The number of ways to choose 12 students from 38 students, C(38,12)
or 2707475148

c. 2 girls are fixed elements and the rest are all boys

The number of ways to choose 10 boys from 15 boys, C(15,10) = 3003.

Edwin