A family with 1 mother, 1 father, and 3 children sit in a car with 2 front seats and 3 back seats. If the mother drives with a child in the front, and the father sits in the back with the other two children, how many seating arrangements are possible?	Choose the correct choice from the following answers:  A) 3  B) 4  C) 6  D) 12  E) 18
In the front seat we have 3 possibilities of children. (C1 or C2 or C3)   In the back seat we have (2!*1)*3 = 6 possibilities ( C1,C2,F / C2,C1,F / C1,F,C2 / C2,F,C1 / F,C1,C2 / F,C2,C1 -&gt; IF C3 is in front seat)   So, 6*3  (2 *1)*3= 
<gadget id="calculator"> (2 *1)*3</gadget>
<output>6</output>
6 possibilities ( C1,C2,F / C2,C1,F / C1,F,C2 / C2,F,C1 / F,C1,C2 / F,C2,C1 -&gt; IF C3 is in front seat)   So, 6*3= 18 (try to figure out to change the possibilities of sitting back the C3 child in the place of C1 or C2 and do the 6 possibilities again and again).   Or, another way to see:   Looking into the back seat:   ( C1,C2,F / C2,C1,F / C1,F,C2 / C2,F,C1 / F,C1,C2 / F,C2,C1) = 6   or +   ( C3,C2,F / C2,C3,F / C3,F,C2 / C2,F,C3 / F,C3,C2 / F,C2,C3) = 6   or +   ( C1,C3,F / C3,C1,F / C1,F,C3 / C3,F,C1 / F,C1,C3 / F,C3,C1) = 6   -------   ANS : 18 :18
<result>E</result>
A family with 1 mother, 1 father, and 3 children sit in a car with 2 front seats and 3 back seats. If the mother drives with a child in the front, and the father sits in the back with the other two children, how many seating arrangements are possible?