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,

1^st digit can take 1 or 2 or 3                                                ---- 3 possibilities

As repetitions are allowed,

2^nd digit can take any of the given 5 digits                        ---- 5 possibilities

3^rd digit can take any of the given 5 digits                         ---- 5 possibilities

4^th 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

Answer (4)