Question

The number of 4 digit numbers greater than 8000 that can be formed with two 5's, three 8's and four 9's is

• A. 51
• B. 50
• C. 52
• D. 49

Answer 1

Answer: (A)

51

a) If the first place is $8$:
The other 3 places can be filled in $3^2$ $=27$ ways (since there are $3$ distinct digits).
There is one number $8555$ and one number $8888$ which are not possible in this case since we do not have those many $5^{\prime }s$ and those many $8^{\prime }s$.
Thus, there are $27-2=25$ numbers.
b) If the first place is $9$:
The other 3 places can be filled in $\left(9\right)$ 3 *3 *3 = $27$ ways (since there are $3$ distinct digits).
There is one number $9555$ which is not possible in this case since we do not have those many $5^{\prime }s$.
Thus, there are $27-1=26$ numbers.
Thus, the answer $=25+26=51$.
Hence, (A) is correct.