Question

How many four digit numbers are there with distinct digits?

• A. $ 5040 $
• B. $ 4536 $
• C. $ 30240 $
• D. $ 5274 $

Answer 1

The Correct Option is B

There are 10 digits in total, but we can only place nine of them in the first position since inserting zero here wouldn't result in a four-digit number. Therefore, the first slot will accept nine different digits.

Again, 9 unique digits will be available for second place, leaving one digit from the arrangement of 10 digits we utilised for first place.

The arrangement of 10 digits we had, out of which one digit was used at first and second place, left us with eight different digits for third place.

From the initial arrangement of 10 digits, out of which we had utilised one-one each at first, second, and third place, we had 7 different digits remaining heading into the fourth position.

Now, in order to calculate the likelihood, we had to double the number of alternative arrangements, since there were nine possible arrangements in the first place, nine more in the second, eight in the third, and seven in the fourth. The total number of arrangements for a four-digit number will thus be

Number of conceivable arrangements at first position, second place, third place, and fourth place.

9x9x8x7 = 4536

A prescribed sequence or series of components or objects can be permuted. Mathematics includes both permutations and combinations as fundamental ideas.

It speaks about the rearranging of elements in an ordered set's linear order. 

The letter nPr is used to represent permutation.

In permutation, the order in which the elements are ordered is important; that is, the elements must be organised in a certain order.

Example: Think about the set A = "{2, 6}". Since there are only two possible arrangements for the components in the given set—{2, 6} and {6, 2}—there will only be two permutations in this case. There is no other way to organise the components of set A besides these two configurations.