Question

How many numbers between $5000$and $10000$can be formed using the digits $1,2,3,4,5,6,7,8,9$each digit appearing not more than once in each number?

• A. $5\times {}^{8}P_3$
• B. $5\times {}^{8}C_3$
• C. $5!\times {}^{8}P_3$
• D. $5!\times {}^{8}C_3$

Answer 1

The correct option is A

$5\times {}^{8}P_3$

Explanation for the correct option:

To find the total numbers:

For numbers greater than$5000$, we can take the first digit as $5,6,7,8,9$

So, ways of choosing the first digit $=5$

Now the rest $3$digits can be chosen from the remaining $8$digits,

Thus ways of choosing $3$digits from $8$digits, when repetition is not allowed $={}^{8}P_3$

Therefore the total numbers $=5\times {}^{8}P_3$

Hence the correct option is A.