RadhaKrishnan 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
Although we could use the permutation formula to answer this question, we can also solve using the Fundamental Counting Principle (FCP, aka the slot method). In fact, we can solve any permutation question using the FCP.
Number of 5-letter words we can makeWe can select the 1st letter in 10 ways
We can select the 2nd letter in 9 ways
We can select the 3rd letter in 8 ways
We can select the 4th letter in 7 ways
We can select the 5th letter in 6 ways
So the total number of ways to construct a 5-letter word =
(10)(9)(8)(7)(6)Number of 4-letter words we can makeWe can select the 1st letter in 10 ways
We can select the 2nd letter in 9 ways
We can select the 3rd letter in 8 ways
We can select the 4th letter in 7 ways
So the total number of ways to construct a 4-letter word =
(10)(9)(8)(7)Ratio of the number of
5-letter code words to the number of
4-letter code words =
(10)(9)(8)(7)(6)/
(10)(9)(8)(7) = 6/1 = 6 to 1Answer: E
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.
RELATED VIDEO