alex.gellatly wrote: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 4-letter code words?

A. 5 to 4
B. 3 to 2
C. 2 to 1
D. 5 to 1
E. 6 to 1

Thanks in advanced

Number of ways to choose 5 different letters out of given 10 letters when the order of chosen letters matters (as for example code word ABCDE is different from BCDEA) = 10P5 = 10!(10 - 5)! = 10 * 9 * 8 * 7 * 6 = 30,240
Number of ways to choose 4 different letters out of given 10 letters when the order of chosen letters matters = 10P4 = 10!/(10 - 4)! = 10 * 9 * 8 * 7 = 5,040

Therefore, required ratio = 30,240/5,040 = 6/1 o r 6 to 1

The correct answer is E.