A house is getting ready for dinner table. There are 15 members in the family, and the butler must assign 10 people to the following positions: 1 main chair, 4 on left side, 4 on right side, and 1 most further away seat. Only 3 of the family members are elderly enough to sit on the main chair, and they will not sit at any other place. The other members can sit on any seat. How many different groupings are possible? Choose the correct choice from the following options.
A) 64585 B) 100 C) 80 D) 59400 E) 789300
3C1 select 1 for main chair from 3 elderly people;   12C4 select 4 people for left side chairs from 12 members (as 3 elderly would like to sit only on main chair  15-3= 
<gadget id="calculator"> 15-3</gadget>
<output>12</output>
12);   8C4 select 4 people for right side chair from 8 members (as 3 are elderly, and 4 we have already selected for left side  15-3-4= 
<gadget id="calculator"> 15-3-4</gadget>
<output>8</output>
8);   4C1 select 1 for the most further away chair from 4 people (again as as 3 are elderly, and 4 we have already selected for left side and 4 for right side chairs   15-3-4-4= 
<gadget id="calculator">  15-3-4-4</gadget>
<output>4</output>
4)   Total # of selection=3C1*12C4*8C4*4C1=59400   Answer: 59400
<result>D</result>
A house is getting ready for dinner table. There are 15 members in the family, and the butler must assign 10 people to the following positions: 1 main chair, 4 on left side, 4 on right side, and 1 most further away seat. Only 3 of the family members are elderly enough to sit on the main chair, and they will not sit at any other place. The other members can sit on any seat. How many different groupings are possible?