## Monday, 24 October 2011

### P&C-5 (CAT-2008)

How many integers greater than 999 but not greater than 4000, can be formed with the digits 0,1,2,3 and 4, if repetition on digits is allowed?
(1) 499         (2)500                (3)375       (4)376       (5)501
Solution follows here:
Solution:
The numbers shall be between 1000 and 4000 (including the two) and are to be formed from the given digits: 0,1,2,3 and 4.
Case-I: Numbers starting with 1 or 2 or 3
Digits considering from left,
1st digit can take 1 or 2 or 3                                                ---- 3 possibilities
As repetitions are allowed,
2nd digit can take any of the given 5 digits                        ---- 5 possibilities
3rd digit can take any of the given 5 digits                         ---- 5 possibilities
4th digit can take any of the given 5 digits                         ---- 5 possibilities
Applying fundamental rule, total number of possibilities = 3*5*5*5 = 375
Case-I: Numbers starting with 4
The only number under this category is 4000                  ---- 1 possibility
Summing up both the cases, total possibilities = 376