How many distinct 5 digit numbers can be formed using the digits … - Vidyadip

Question

How many distinct 5 digit numbers can be formed using the digits $3,2,3,2,4,5$.

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Answer

5 digit numbers are to be formed from $2,3,2,3,4,5$.
Case I: Numbers formed from 2, 2, 3, 4, 5 OR 2, 3, 3, 4, 5
Number of such numbers $=\frac{5 !}{2 !} \times 2$
$
\begin{aligned}
& =5 ! \\
& =120
\end{aligned}
$
Case II: Numbers formed from 2, 2, 3, 3 and any one of 4 or 5
Number of such numbers $=\frac{5 !}{2 ! 2 !} \times 2=60$
Required number $=120+60=180$
$\therefore 180$ distinct 5 digit numbers can be formed using the digit $3,2,3,2,4,5$.

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