Need help on question from professor

Suppose that a class contains 15 boys and 30 girls, and that 10 students are to be selected at random for a special assignment. Find the probability that exactly 3 boys will be selected. I used the combination rule to figure out the combinations of r objects within the n objects that could be found using the nCr formula.

Combined

Known Numbers

Boys

455

Boys

15

Girls

2035800

Girls

30

Total

3190187286

Total

45

Probability

.29035568

Boys needed

3

Girls needed

7

Students needed

10

The combination formula was used to determine the number of boy combinations.

Combination formula-nCr=n!/(n-r)!r!

There are 455 different boy combinations

The combination formula was used to determine the number of girl combinations.

Combination formula- nCr=n!/(n-r)!r!

There are 2,035,800 girl combinations

The total combination of numbers were used to solve the formula

45C10=45!/(45-10!)!(10!)=3190187286

3,190,187,286 Total Numbers of Combinations

To determine the number of combinations for exactly 3 boys, the number of boy combinations is multiplied by the number of girl combinations. This number is then divided by the total number of combinations.

455*2035800 / 3190187286=.29035568 =29%

Answer: The probability of getting exactly 3 boys on a random selection of 10 students is 29%.

Ashley: How did you arrive at the numbers that you report in your posting (for each case)? Why did you use combinations and not permutations? What other concept, besides combinations, did you use to compute the final percentage of 29%?