Question

A password for a site consists of four digits followed by 2 letters. The letters A and Z are not used and each digit or letter may be used more than once. How many unique passwords are possible?

chapter: permutations and combinations ​

Answer 1

Answer:

479,952

Step-by-step explanation:

26-2=24*2=48

9999*48=479,952

Answer 2

Given:

A password consitst $4$ digits and followed by  $2$ letters.

And also given the alphabets $A,Z$ should not be used.

Therefore, we have only $26-2=24$ alphabets to be used.

And we have $10$ digits from $0$ to $9.$

Therefore:

The number of unique passwords are =$Digit\times Digit\times Digit\times Digit\times Letter\times Letter$

$=10\times10 \times 10 \times 10\times 24\times 24$

$=5,760,000$

Therefore, The number of unique passwords are $=5,760,000.$