Question

How many numbers lying between $100$ to $1000$ can be formed with the digits $0,1,2,3,4,5$, if the repetition of the digits is not allowed?

• A. $50$
• B. $70$
• C. $90$
• D. $120$

Answer 1

Answer: (D)

$120$

No. between $100$ and $1000$ will be $3$ digits no.'s. $3$ digit no. will be formed form the digits $0,1,2,3,4,5$. But these include no. starting with $0$ like $05,01\dots \text{etc.}$ which actually $2$ digit no's.

$\therefore \text{Required no.}=\text{Total 3 digit no.}-\text{3 digit no.'s which have 0 in the begining}.$

Total digits in $0,1,2,3,4,5,6=6⟹n=6$

Herewe have to form $3$ digit number, $r=3.$

$\text{Total no. of 3 digit no.'s}{=}^n{P}_r{=}^6{P}_3=120$.