In a certain mathematical activity, we start with seven cards, each with a different prime number written on it. These seven cards are randomly put into three boxes in the following way: one box must get four cards, one must get two, and one gets only one. Then, for each box, we find the product of all the cards in the box, and that’s the “number” of the box. Then, we put those three numbers in order, from lowest to highest, and that is our set. How many different sets R can be created from this process? Choose the correct choice from the following answers:
A) 35
B) 105
C) 210
D) 420
E) 630
R=7C4 * 3C2 = 105 Answer B.   7C4 ways to choose 4 numbers for Box 1   3C2 ways to choose 2 numbers for Box2   1 way for Box 3 .   every combination will give a different product and can be arranged least to highest only in one way .105
<result>B</result>
In a certain mathematical activity, we start with seven cards, each with a different prime number written on it. These seven cards are randomly put into three boxes in the following way: one box must get four cards, one must get two, and one gets only one. Then, for each box, we find the product of all the cards in the box, and that’s the “number” of the box. Then, we put those three numbers in order, from lowest to highest, and that is our set. How many different sets R can be created from this process?