SOLUTION: If a family has seven children, in how many ways could the parents have four boys and three girls?

There are three ways to work it:

First way:

There are 7 birth orders, so we can choose the 4 birth orders
for the boys in C(7,4)=35 ways and the 3 remaining birth orders 
would be for the girls.

Answer C(7,4) = 35

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Second way:

Notice that the answer would be the same if we choose the 3 birth
orders for the girls in C(7,3)=35 and the 4 remaining birth orders 
would be for the boys.

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Third way:

Also notice that it would be the same as the number of distinguishable
arrangemenents of the 7-letter "word" BBBBGGG

 =  = 35

Edwin