Question

The number of numbers greater than a million that can be formed with the digits 2, 3, 0, 3, 4, 2 and 3 is

• A. 360
• B. 340
• C. 370
• D. None of these

Answer 1

Answer: (A)

Any number greater than a million must be of 7 or more than 7 digits. Here number of given digits is seven, therefoer we have to form numbers of seven digits only.
Now there are seven digits of which 3 occurs thrice and two occurs twice.
$\therefore$ number of numbers $\frac{7!}{2!3!}=420$
But this also includes those numbers of seven digits whose first digit is zero and so in fact they are only six digit numbers.
Number of numbers of seven digits having zero in the first place $1\times \frac{6!}{2!3!}=60$
Hence required number $=420-60=360$formed