Question

How many numbers of four digits can be formed with the digits $1,2,3,4$ and $5$ when repetition of digits is not allowed

• A. $20$
• B. $120$
• C. $4$
• D. $5$

Answer 1

The correct option is B $120$

Split the work into two independent works -

(i) Choosing 4 digits out of the set of 5 which can be done in ${}^5{\text{C}}_4$ ways .

(ii) Now arrange these 4 chosen digits to form new number as there are no restriction on how to arrange them the total ways will be equal to $4!$.

Hence the total number of 4 digit numbers are $=$ ${}^5{\text{C}}_4$ $\times$ $4!$ $=120$