Question 356904
This problem is easier if you consider the problem in two steps:
1. Pick a team of 5 members
2. From the members of that team, pick a captain.<br>
For picking a team, this is a problem of figuring out how many sets of 5 are possible when picking from a group of 20. This is a combination which we can find using:
{{{(20*19*18*17*16)/(1*2*3*4*5)}}}
The 4*5 cancels the 20 and the 2*3 (or 6) cancels with the 18 (leaving 3):
19*3*17*16 = 15504
So there are 15504 possible teams of 5 which can be formed from the 20 children.<br>
Now we can pick the captain. On each of these 15504 teams, there are 5 possible choices for captain. So there are 15504*5 = 77520 possible ways of picking a team of 5 with one of the five being captain.<br>