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.