Aptitude Hack#35(30-3-19)

Question:
Given digits 2, 2, 3, 3, 3, 4, 4, 4, 4 how many
distinct 4 digit numbers greater than 3000 can
be formed?

A) 50
B) 51
C) 52
D) 54

Answer B) 51

Explanation:

As the number is greater than 3000.

So Thousand's place can have 3 or 4.

Let's consider the following two cases

Case (I) when a thousand's place is 3.

      3 a b c

 If there is no restriction on the number of two's,

Three’s and four's. Then each of a, b, c can be

Filled with 2 or 3 or 4 each in 3 ways.

So 3 x 3 x 3 = 27 numbers are there. Out of

Which 3222, 3333 are invalid as 2 can be used

Twice & 3 can be used thrice only so the number of such valid

 numbers beginning with 3 are 27 - 2 = 25.

Case (Il) When the thousand's place is 4

    4 a b c

Without restriction on the number of 2's, 3's and 4's

a, b, c (as explained in case I) can be filled in 27 ways.

Out of these 27 numbers, 4 2 2 2 is only invalid

as two have to be used twice only.

So valid numbers are 27 - 1 = 26.

Total numbers from Case (I) & Case (Il)  

=>25 + 26 = 51.