Question

How many numbers between $5000$ and $10,000$ can be formed using the digits $0,1,2,3,4,5,6,7,8,9$ 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 $5{\times }^8{P}_3$

$1^{st}$ digit can be any of $5,6,7,8,9=5$ ways

$2^{nd}$ digit can be any of remaining of 9 digits (excluding $1^{st}$ digit) = $9$ ways

$3^{rd}$ digit = $8$ ways, $4^{th}$ digit = $7$ ways

$\therefore$ answer is $5\ast 9\ast 8\ast 7=2520$