Question 962557
a group of five children has to be chosen from a form of eight boys and twelve girls.in how many ways can the selection be made if the group must contain at least two boys and two girls? 
<pre>
That's either 3 girls and 2 boys or 2 girls and 3 boys.

Case 1:  3 girls and 2 boys

Choose the 3 girls 12C3 = 220 ways and the 2 boys 8C2 = 28 ways.
That's 220*28 = 6160 ways.

Case 2:  2 girls and 2 boys

Choose the 2 girls 12C2 = 66 ways and the 3 boys 8C3 = 56 ways.
That's 66*56 = 3696 ways.

Grand total 6160+3696 = 9856 ways.

Edwin</pre>