Question
How many $5$ digit numbers can be formed using all the digits $2, 5, 0, 7$ and $9$ ?
✓
Answer
If 5 digit numbers are to be formed using all the digits $2,5,0,7,9$ then digit $0$ should not be in the first place.
Therefore, excluding digit $0$ , one of the four digits can be placed in the first place in ${ }^{4} P_{1}$ ways.
Now, after arranging one digit from $2,5,7$ or $9$ in the first place, remaining $4$ digits (including $0$ ) can be arranged in remaining $4$ places in ${ }^{4} \mathrm{P}_{4}$ ways.
$ \therefore \text { Total Permutations } ={ }^{4} \mathrm{P}_{1} \times{ }^{4} \mathrm{P}_{4}$
$ =4 \times 4 !$
$ =4 \times 24$
$ =96 $
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