Question about probability distribution homework

[jerry_v]

I am stuck on this question in my textbook:

A child removes the name cards on ten wrapped Christmas gifts of which six are for the Changs and four are for the Andersens. If the presents are distributed to the two families without reopening the packages, what is the probability that the Changs get five of the presents originally intended for them?

I tried using using the hypergeometric distribution but am not getting the correct answer (which is 12/105)
Any pointers/help would be greatly appreciated

 

[pka]

A child removes the name cards on ten wrapped Christmas gifts of which six are for the Changs and four are for the Andersens. If the presents are distributed to the two families without reopening the packages, what is the probability that the Changs get five of the presents originally intended for them?

Can you evaluate \(\dfrac{\dbinom{4}{3}\dbinom{6}{1}}{\dbinom{10}{4}} ~\large?\)

 

[jerry_v]

Hey, thanks for the reply.
I assume its (4C3)(6C1)/(10C4)? May I ask how the bottom values (3, 1, 4) come from? thanks

 

[pka]

.
I assume its (4C3)(6C1)/(10C4)? May I ask how the bottom values (3, 1, 4) come from? thanks

If the Andersens' family get three gifts meant them & one meant for the Changs, then the other gifts include one meant for the Andersens.
BTW: \(\dfrac{4}{35}\)=\(\dfrac{12}{105}\)