A four character password consists of one letter of the alphabet and three different digits between 0 and 9 inclusive. The letter must appear as the second or third character of the password. How many different different password are possible?

a. 5040 b.18720 c.26000 d.37440 e. 52000

E. 52,000

I solve it based on number of possibility each letter or digit can be inserted.

If the letter in the 2nd digit: 10 X 26 X 10 X 10 = 26,000 possibilities

If the letter in the 3rd digit: 10 X 10 X 26 X 10 = 26,000 possibilities

Add them up = 26,000 + 26,000 = 52,000 (E)

Since the question mentioned â€śThree different digitsâ€ť we should reduce the number of digits:

If the letter in the 2nd digit: 10 X 26 X 9 X 8 = 18,720 possibilities

If the letter in the 3rd digit: 10 X 9 X 26 X 8 = 18,720 possibilities

Add them up = 18,720 + 18,720 = 37,440(D)

I did this in the same way but the answer is 37440

so.

The answer is 37400

2*26*10*9*8

â€ś2â€ť means that the letter can be in the 2nd or the 3rd position

â€ś26â€ť means that there have 26 different letters can be choosed

10*9*8 comes from the phrase â€śthree *different* digitsâ€ť, as it indicates that the remained three positions should be put into three different digits. Thus, the first position gets ten choices, leading the second has 9 choices, and lastly, the final empty position only gets 8 choices.

So that the equation is 10*9*8

2*26*10*9*8 = 37400