How many different numbers lesser than 10000 can be formed from the digits 1,3,6,8,7 and 9, if no digit is repeated ?

Explanation

The number less than 1000 can be
(i) One digit number
(ii) Two digits numbers
(iii) Three digits numbers
if no digit is repeated, then
(i) Number of one digit =5
(ii) Number of ways of filling Unit's place =5
Number of ways of filling ten's place=4
`therefore ` Total numbers of two digits `=5xx4=20`
(iii) Number of ways of filling unit's place =5
Number of ways of filling ten's place=4
Number of ways of filling hundred's place =3
`therefore` Total numbers of three digits `=5xx4xx3=60`
Hence , by the prinicple of addition total numbers formed is `5+20+60=85`