Question

How many 4 digit numbers greater than 5000 can be formed by using the digits 2, 3, 5, 6, 7 and 8 such that none of the digits are repeated?

• A. 216
• B. 240
• C. 360
• D. 120

Answer 1

The correct option is B 240

When none of the digits are repeated:

The hundred’s place can be filled by any of the digits: 2, 3, 5, 6, 7 or 8 except the one which has already been used at the thousand’s place, so it can be filled in 5 ways.

Similarly tens’ place can be filled in 4 ways: only those 4 numbers which have not been use either at hundred’s or thousand’s place.

Unit’s place can be filled in only 3 ways. So, total number of nos. Possible =$4\times 5\times 4\times 3$= 240