Thread: Permu

let A be a set of 4 digit nos a1,a2,a3,a4 where a1>a2>a3>a4, then n(A) is equal to

This can be solved by using combination. Make this a function where X={a1,a2,a3,a4} and Y={0,1,2,...9}. All you have to do is pick 4 numbers from Y. You dont even need to think about the order because the biggest number automatically becomes a1 and the smallest number becomes a4.

Hello, prasum!

Very sloppy wording . . .

composed of the digits
and each digit is used once.

* .The problem said that the 4-digit numbers are: .
. . Therefore:. . (duh!)

* .If the digits can be repeated:.

Having said all that:.


BTW the inequality was given to indicate that the digits are distinct.

If the digits were or , the answers would "depend".

Originally Posted by prasum

let A be a set of 4 digit nos a1,a2,a3,a4 where a1>a2>a3>a4, then n(A) is equal to

I think that reply #2 is correct.
This question is about what is known as strictly sorted natural numbers with descending digits.
Example: 7421 and not 7412.
Any set of four distinct digits corresponds to a strictly sorted natural number with descending digits.