If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 3-letter code words? Pick one
A) 36
B) 38
C) 40
D) 42
E) 44
Method #1: Using the permutation formula   # of 5 letter code words:   nPr = n! / (n – r)! = 10! / (10 – 5)! = 10*9*8*7*6   # of 3 letter code words:   nPr = 10! / (10 – 3)! = 10*9*8   # of 5 words / # of 4 words = (10*9*8*7*6)/(10*9*8)= 
<gadget id="calculator">(10*9*8*7*6)/(10*9*8)</gadget>
<output>42</output>
42   42
<result>D</result>
If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 3-letter code words?