Question

Number of Whole number's less than $1000,$ that can be formed using the digits $0,1,2,3,4,5$ is

• A. $131$, when repetition is not allowed
• B. $216$, when repetition is not allowed
• C. $216$, when repetition is allowed
• D. $347$, when repetition is allowed

Answer 1

Answer: (A), (C)

The correct options are
A $131$, when repetition is not allowed
C $216$, when repetition is allowed

Case $1:$ When repetition is not allowed.

The number of one-digit numbers is $6$.
The number of two digit numbers is $5\times 5=25.$
The number ot thee-digit numbers is
$5\times 5\times 4=100.$
Hence, the total number are is $=6+25+100=131.$

Case $2:$ When repetition is allowed.

The number of one-digit numbers is $6$.
The number of two digit numbers is $5\times 6=30.$
The number ot thee-digit numbers is
$5\times 6\times 6=180.$
Hence, the total number are is $=6+30+180=216.$