Possiblity

[patrickgong6688]

A four character password consisits of one letter of the alphabet and three different digits between 0 and 9, nclusive. The letter must appear as the second or third character of the password .How many different passwords are possible.?
A5040 B18720 C26000 D37440 E52000
The answer is D
Can someone give me a reply ?

[messi10]

Hi Patrick,

Please specify the source of your question. They must be from a valid source. Please check the forum rules to make sure that it is not from a banned source.

Also, please tell us what you do not understand about the question

Thanks

Sunil

[patrickgong6688]

Hi there ,

This question came from a book which was bought in china.This book was writen by a famous chinese teacher who tought GMAT Quantitative in a prestigious school which is Neworiental for many years.His name is Chenxiangdong.
For this question , I counted as below but it did not work . 10X35X8X7+10X9X34X7=41020. Did I miss something?

Best regards,
Patrick

[messi10]

Hi,

You have to consider two scenarios:

1) The letter appears as the 2nd character of the password:

10 x 26 x 9 x 8 = 18720

2) The letter appears as the 3rd character of the password:

10 x 9 x 26 x 8 = 18720

Adding the above, you get 37440.

I can see that your logic is OK except that you have taken 35 and 34 as the 2nd and 3rd character. I am assuming that you have done this because you counted the letters and the numbers for that position. This is not right. The questions clearly states that the password must have a letter. By taking 35 and 34, you are including the passwords that contain no letters at all.

Hope this makes sense

Regards

Sunil

[jnelson0612]

As always, thanks Sunil!