Question

Alisha has forgotten the passcode of her mobile consisting of 4 distinct digits. What are the number of different combinations she can make for retrieving the passcode?

• A. $720$
• B. $560$
• C. $5040$
• D. $5540$

Answer 1

The correct option is C $5040$

Her mobile passcode must be formed using the digits $0,1,2,3,4,5,6,7,8,9.$

Also, it is given that it has $4$ digits and each digit is different.

First digit can be choosen in $10$ different ways, taking any of the $10$ digits.

Since digits are distinct, number of ways of choosing second, third and fourth digit is $9,8,$ and $7$ respectively.

This can be equal to filling of $4$ vacant places as shown:


So,
Maximum number of attempts for unlocking the mobile is equal to total number of ways of choosing $4$ digits of passcode is $=10\times 9\times 8\times 7=5040.$