Question

No. of such numbers between 5000 and 10000 that 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 is

• A. $5{\times }^8{P}_3$
• B. $5{\times }^8{C}_8$
• C. $5!{\times }^8{P}_3$
• D. $5!{\times }^8{C}_3$

Answer 1

The correct option is A $5{\times }^8{P}_3$

Numbers between $5000$ and $10000$

Digits $1,2,3,4,5,6,7,8,9$

First digit can be $(5,6,7,8)$ and also $9$

Number of ways $=4+1=5$

Rest there can be any of the digits

Arrangements $={}^8{P}_3$

Total possiblities $=5\times {}^8{P}_3$