Question

Correct answers only please!

A student number system for a county requires that the student number be 5 characters. The first 3 characters are any single digit number, but no number can repeat and the last 2 characters must be letters, but no letter can repeat. How many unique student numbers are possible?

A. 1,370

B. 131,040

C. 250,000

D. 468,000

Answer 1

Answer: D) 468,000

Explanation:

1st character has 10 choices (numbers 0 - 9)

2nd character has 9 choice (numbers 0 - 9 excluding 1st number)

3rd character has 8 choices (numbers 0 - 9 excluding 1st & 2nd numbers)

4th character has 26 choices (A - Z)

5th character has 25 choices (A - Z excluding 4th character)

Multiply 1st & 2nd & 3rd & 4th & 5th characters

10 × 9 × 8 × 26 × 25 = 468,000