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?
Pick one
A) 80 B) 288 C) 44 D) 576 E) 288^2
Case-1: 3 Boys and 2 Girls are taken   Selection of 3 boys and 2 girls can be done in 4C3 * 4C2   Arrangement will look like B G B G B and Such arrangement of 5 individual can be done in desired manner in 3!*2! ways = 12 ways   No. of arrangement = 4C3 * 4C2 *3!*2! = 4*6*12= 
<gadget id="calculator">4*6*12</gadget>
<output>288</output>
288   Case-2: 2 Boys and 3 Girls are taken   Selection of 2 boys and 3 girls can be done in 4C2 * 4C3   Arrangement will look like G B G B G and Such arrangement of 5 individual can be done in desired manner in 3!*2! ways= 12 ways   No. of arrangement = 4C2 * 4C3 *3!*2! = 4*6*12= 
<gadget id="calculator">4*6*12</gadget>
<output>288</output>
288   Total Ways of Taking Photograph of 5 in desired manner= 288 + 288= 
<gadget id="calculator">288 + 288</gadget>
<output>576</output>
576 ways   Answer: Option 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?