# Digits help?

**Question**

How many 3 digit positive intergers can be formed using the digits 2,3,4,5,6,7,8 is the units digit is 2 and no digit is repeated within the interger????

12

15

24

30

36

**Answer**

The “2” is used for the last digit or unit digit.

We are left with ‘6’ integers. We want ‘3’ digit numbers.

So, from these 6 intergers we “choose” pairs of “2 integers” and then “permutate” them to “fill the first two digits of our two digit number”.

C(6 , 2 ) = Number of ways to “choose” the “pair of two digits for our 3 digit number whose last digit is 2”

2! = The number of ways we can “permutate” or “rearrange” our chosen pair of two digits above in order to form our 3 digit number whose last digit has been fixed as 2.

where,

C(n , r) =[ n! ] / [ (n – r)! r! ]

The number of ways = C(6 , 2) x 2!

= 15 x 2

= 30

So there are 30 such integers.