Problem Solving Combinations

In summary, the number of different groups that contain exactly four girls and five boys is 11639628. For part b, the number of groups of 14 with an equal number of boys and girls is the same as part a. For part c, the total number of groups with more boys than girls is the sum of the choices from 5-0, 4-1, 3-2, 2-3, 1-4, and 0-5.
  • #1
Draggu
102
0

Homework Statement


There are 15 boys and 19 girls in a room.
a) Find the number of different groups that contain exactly four girls and five boys.
b) How many groups of 14 have an equal number of boys and girls?
c) How many groups of 5 have more boys than girls?


Homework Equations





The Attempt at a Solution


a) C(19,4) * C(15,5)
=11639628

b & c I have no idea where to start.
 
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  • #2
Isn't b just like a? If you have 14 people with equal numbers of boys and girls then how many boys? Girls?

And for c, what are the choices that qualify from 5-0, 4-1, 3-2, 2-3, 1-4, 0-5. Figure them out and add them up.
 
  • #3
Can you provide more context or information? How many total people are in the room? Are there any restrictions on the group sizes or combinations? Without more information, it is difficult to provide a solution for parts b and c.
 

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