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 1

The correct option is B 51

As the number is greater than 3000 . So, thousand's place can be either 3 or 4.

Let consider the following two cases.

Case (1) : When thousand's place is 3.

3 a b c
If there is no restriction on 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 $\times$ 3 $\times$3=27 numbers are there. Out of which 3222,3333 are invalid as 2 can be used twice & three thrice only so number of such valid numbers begining with 3 are
27-2 = 25 ...(1)

Case (2) : When thousand's place is 4
4 a b c
Without restriction on number of 2's, 3's, and 4's a, b, c (as explained in case 1 ) 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 ...(2)
Total numbers from case (1) & case (2)
25+26 = 51.