Question

How many different 5 digit PIN codes are there that only include the digits 4,5,6,7,8 and 9

Answer 1

Given:

Digits are 4,5,6,7,8 and 9.

To find:

The number of ways to form a 5 digit pin using the given digits.

Solution:

We have,

Total number of given digits = 6

Number of required digits to form a 5 digit pin = 5

Number of ways to arrange 5 digits from 6 digits is

$^6P_5=\dfrac{6!}{(6-5)!}$           $[\because ^nP_r=\dfrac{n!}{(n-r)!}]$

$^6P_5=\dfrac{6\times 5\times 4\times 3\times 2\times 1!}{1!}$

$^6P_5=6\times 5\times 4\times 3\times 2$

$^6P_5=6\times 5\times 4\times 3\times 2$

Therefore, the number of ways to form a 5 digit pin using the given digits is 720.