SOLUTION: in how many ways can a group of 5 boys be chosen from a class of twenty boys if the class captain has to be included

Question 922183: in how many ways can a group of 5 boys be chosen from a class of twenty boys if the class captain has to be included
Answer by Hawksfan(61) (Show Source): You can put this solution on YOUR website!
When order matters, It is a permutation.
If order doesn't matter, It is a combination.
In this case, order DOESNT matter. It is a combination.
n C k = n!/(n-k)!* k!
n is the number of items
k is the number in the subgroup
20 C 5 = 20!/ (20-5)! 5!
(20 *19* 18 *17* 16 * 15!)/15!* 5!
parenthesis don't need to be there but with the computer its hard to
show what numbers are being divided by what.

divide out the 15! to get
20 * 19 * 18 * 17 *16/ 5!
20*19*18*17*16/20*6
5! = 120... now divide by 20
19*18*17*16/6
divide by 6
19*3 *17 * 16 = 15504

RELATED QUESTIONS
In how many ways can two students be chosen as monitors, one from the girls and another... (answered by ewatrrr)

A mathematics class consist of 15 boys and 25 girls. A.In how many ways can the position (answered by stanbon)

a group of five children has to be chosen from a form of eight boys and twelve girls.in... (answered by Edwin McCravy)

A class consists of 12 boys and 15 girls. How many different committees of four can be... (answered by ikleyn)

A class has 8 boys and 4 girls. A committee of 3 has to be chosen. In how many ways can... (answered by ewatrrr)

A teacher has 10 boys and 12 girls in her grade school class. In how many ways can she... (answered by sudhanshu_kmr)

Q15 In how many ways can we distribute seven apple and six oranges among 4 children so... (answered by lynnlo)

From a class of girls and boys, the probability that one student chosen at random will... (answered by stanbon)