Question

The number of positive integers which can be formed by using any number of digits from $0,1,2,3,4,5$ without repetition

• A. $1200$
• B. $1500$
• C. $1600$
• D. $1630$

Answer 1

The correct option is D $1630$

One digit positive integers are $1,2,3,4,5$ $=5$ positive integers

Two digits with $0$

_ _0

So First place can be filled in 5 ways.

Total $=5$

Two digit number where $0$ is not included

_ _

$=5\times 4=20$

Three digit number _ _ _

First block can be filled in $5$ ways (0 would n't be there)

Second Block in $5$ ways and third in $4$ ways

Total $5\times 5\times 4=100$

Similarly Four digit number $=300$

Five digit number $=600$

Six digit number =$600$

Total $=5+20+5+300+600+600=1630$