Question

How many numbers with not more than three digits can be formed using only the digits $1$ through $7$ with no digit used more than once in a given number?

• A. $259$
• B. $249$
• C. $257$
• D. $252$
• E. $269$

Answer 1

The correct option is A $259$

Numbers can be with $1$ digit, $2$ digit and $3$ digit are formed by $1,2,3,4,5,6,7$
Therefore, required numbers are ${}^7{P}_1{+}^7{P}_2{+}^7{P}_3=259$.