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How many 4 digit numbers can be formed from the digits 1,2,3,4,5,6 and 7 which are divisible by 5 when none of the digits are repeated?

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Number of ways $4$ digit numbers can be formed from the digits $1,2,3,4,5,6,7$ will be $(\color{purple}{\text{without repetition}})$
 

= $\color{violet}{840 \hspace{0.1cm} ways}$

Now, the number should be divisible by $5$

$\color{chocolate}{\text{Divisibility Rule of 5 says that }}- \color{maroon}{\text{The last digit of the number should be}}$ $\color{red}{0}$ $\color{maroon}{or}$ $\color{red}{5}$

∴ We'll fix $5$ at the unit place

Remaining digits can be arranged in

                                   



= $\color{pink}{120 \hspace{0.1cm} ways}$

∴ $\color{red}{120} \color{green}{\text{  4 digit numbers can be formed from the digits 1,2,3,4,5,6 and 7}}$

$\color{green}{\text{which are divisible by 5 when none of the digits are repeated}}$

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