A photographer is to take group photographs of a class of students for the school magazine such that each photograph should have five students. If there are four girls and four boys in the class and each photograph must not have two girls or two boys standing together, how many different photographs can the photographer take?
Select the correct option:
A) 80
B) 288
C) 4^4
D) 576
E) 288^2
The condition that TWO boys or TWO girls cannot be together means they should be alternate..   Total five means 3 of one and 2 of other..   1) choose 3 girls and arrange them... 4C3*3! = 4!= 24   2 boys can be choosen in 4C2 and arrange them in 2! Ways... 4C2*2!= 12   Total ways = 24*12 = 288..   2) same as above.. 2 girls and 3 boys.. 288   Total 288*2= 
<gadget id="calculator">288*2</gadget>
<output>576</output>
576   ANS:576
<result>D</result>
A photographer is to take group photographs of a class of students for the school magazine such that each photograph should have five students. If there are four girls and four boys in the class and each photograph must not have two girls or two boys standing together, how many different photographs can the photographer take?