Question

The total number of natural numbers of six digits that can be made with digits $1,2,3,4$ , if all digits are to appear in the same number at least once, is $?$

• A. $1560$
• B. $840$
• C. $1080$
• D. $480$

Answer 1

The correct option is A

$1560$

Formation of the number :

We need to find the number of natural numbers of six digits out of four digit, i.e. $1,2,3,4$.

Thus, the $4$ digits are fixed and the other two digits could be same or different.

If both digits are same, then number of ways $={}^{4}C_1\times \frac{6!}{3!}$

$=480$

If both digits are different then number of ways$={}^{4}C_2\times \frac{6!}{2!\times 2!}$

$=1080$

Therefore, total number of ways $=480+1080$

$=1560$

Hence option (A) is the correct option.