Answer with explanation:
Number of earring boxes that Mary has =50
Dimension of each box = 1 inch× 1 inch × 1 inch=1 cubic inches
⇒Number of rectangular prisms, each with a different – sized base, that Mary can make by stacking all of the earring boxes
=Then, the Dimension of Box will be as follows
= [ Length=1 inch , 1 inch≤Base≤50 inch, Height =1 inch]
=[(1,1,1), (1,2,1),(1,3,1),(1,4,1),(1,5,1),(1,6,1),(1,7,1),(1,8,1),(1,9,1),(1,10,1),(1,11,1),(1,12,1),.....,(1,50,1)]
=So, there will be , 50 different Rectangular prism ,earrings.
⇒⇒There is another way of looking at the Question.If you have to ,use each earring once then,Number of rectangular prism each with different size
=[(1,1,1), (1,2,1),(1,3,1),(1,4,1),(1,5,1),(1,6,1),(1,7,1),(1,8,1),(1,9,1)], 5 earrings will be left,when stacked together will form the combination in the set Provided.
→So, total number of Distinct earring = 9 Rectangular prisms
Otherwise,→ number of Distinct Earring =50
Option D: 50