Question

How many permutations of three different digits are there, chosen from the ten digits $0$ to $9$ inclusive?
A.$84$
B.$120$
C.$900$
D.$504$

Answer 1

Hint: Permutation is an ordered combination- an act of arranging the objects or numbers in the specific favourable order. Here, we will follow the basic concepts of three digits mathematical terms and apply the permutations for the given set of numbers.

Complete step-by-step answer:
The total different three-digit number can be arranged by –
The very first or the left most place of the number cannot be occupied by $0$ (zero), as we require a three-digit number and so will use non-zero numbers only. So, this place can only be filled by any of the $9$ digits from $1,2,.....9$ Hence, the hundredth place can only be occupied in $9$ different ways.
Now, ten’s place can be occupied any of the ten digits from$0,1,2,.....9$. So, it can be arranged in $10$ different ways.
Similarly, for a unit's place- it can occupy any of the ten digits from$0,1,2,.....9$. So, it can be arranged in $10$ different ways.
Therefore, the total arrangements of the three different digits will be –
$ = 9 \times 10 \times 10$
Simplifying the above equation-
The total arrangements $ = 900$
Hence, from the given multiple choices- the option C is the correct answer.

Note: Know the permutations and combinations concepts properly and apply accordingly. In permutations, specific order and arrangement is the most important whereas a combination is used if the certain objects are to be arranged in such a way that the order of objects is not important.