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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.

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