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
E) 6 to 1
E
E baby , E …. (10C5/10C4)=6/1
(B) 10C5/10C4 =3:2
Hey syed, you forgot the basic arithmetic yaar !!
E
e
The correct answer is 10P5/10P4 = 6/1.
hence E
Thats incorrect. Then it would mean the number of 4 letter codes are lesser then the number of 5 letter. In fact, we can make more 4 letter codes than 5 letter codes.
By the way, the answer is:
10P5/10P4 = 4! / 5! = 24/120 = 1/5
The answer options are incorrect!
Please let me know of any wrongs
-Venkat
Syed & Ban_GMAT – check yoru calculations —> 10C5 / 10C4 = 6/5 and NOT 3/2 or 6/1
Answer shoutd be 6:1
There are 10*9*8*7*6 ways to choose a 5 digit code and 10*9*8*7 ways for a 4 digit code….divide this, you will get 6:1
6 to 1
E
Ans options are incorrect!!!!!!!!
ans should be 1/5. I agree with venkata.subramani
10/1
There’s nothing in the question to say that letters can’t be repeated (unless I’m missing something? Maybe a particular convention for the definition of ‘code’ as prohibiting repetition?).
If letters can be repeated, then there’s 10^5 codes with 5 letters, and 10^4 codes with four letters. 10^5/10^4 = 10
Best,
A.
excellent explaination venkat..
even i was wondering the same..all the options present depict that the number of codes formed by 4 digit would be less whereas the case is quite opposite..
E