CBSE Class 11-science Answered
1) In the four digit number 0 cannot appear in the thousand’s place. So, thousand’s place
can be filled in 5 ways (using 1,2,3,4 or 5). Since repetition of digits is not allowed and 0 can be used at hundred’s place, so hundred’s place can be filled in 5 ways. Now, any one of the remaining four digits can be used to fill up ten’s place. So ten’s place can be filled in 4 ways. One’s place can be filled from the remaining three digits in 3 ways.
Hence, the required number of numbers = 5 x 5 x 4 x 3 = 300
2) For a four digit number we have to fill up four places and 0 cannot appear in the thousand’s place can be filled in 5 ways. Since repetition of digits is allowed, so each of remaining three places hundred’s, ten’s and one’s can be filled in 6 ways.
Hence, the required number of numbers = 5 x 6 x 6 x 6 = 1080.