Question

The number of numbers lying between 99 and 1000 which can be formed using the digits 2, 3, 7, 0, 6, 8 when no digit is being repeated is

• A. 102
• B. 120
• C. 100
• D. None of these

Answer 1

The correct option is C 100

Digits are 2, 3, 7, 0, 6, 8 i.e. six in all.
We have to form a number between 99 and 1000. Clearly, they will be of three digits and their number will be
${}^6{P}_3=6\times 5\times 4=120$
Out of these, we have to exclude those numbers of 3 digits which have zero in the first place.
When the first place is filled by 0, remaining numbers can be arranged in ${}^5{P}_2$ ways.
Their number is ${}^5{P}_2=5\times 4=20$
$\therefore$ The required number is 120-20=100