The Gateway to Computer Science Excellence
0 votes

in Combinatory by Loyal (8k points)
retagged by | 248 views

1 Answer

0 votes

This should be easy if you break it into no digit repeating, one digit repeating and two digits repeating (you cannot have 3 digits repeating in a 5 digit number).

There are 9P5 = 15,120 permutations without any digit repeating.

There are 9C4 * 5!/2! = 7,560 permutations with one digit repeating. 9C4 for choosing 4 digits letting one repeat and 5!/2! for arranging the 5 digits.

Similarly, there are 9C3 * 5!/2!^2 = 2,520 permutations with two digits repeating.

Overall, there are 25,200 5 digit numbers with no digit repeating more than twice. This is still only just about 1/4th of 90,000 possible 5 digit numbers. 

Source:Quora. I myself haven't worked it out. You can refer d link mentioned below for more information.

by Boss (13.8k points)

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
50,737 questions
57,375 answers
105,292 users