Question

How many six digit numbers can be formed by using the digits $1,2,3$ and in which at least one digit is different

• A. $724$
• B. $725$
• C. $726$
• D. $720$

Answer 1

Answer: (C)

$726$

Given that there are $3$ numbers $1,2,3$ using which we need to form $6$ digit numbers so that at least one digit is different.

At least one digit is different $=$ Total $-$ No digit is different.

$\Rightarrow$ Total possible numbers $=3\times 3\times 3\times 3\times 3\times 3=3^6$

$=729$

$\Rightarrow$ Numbers in which no digit is different $={}^3{C}_1=3$

(All $1,$ All $2,$ All $3$)

$\Rightarrow$ Required $=729-3=726.$

Hence, the answer is $726.$