Question

There are $10$ balls of different colors out of which arrangement of $4$ balls are done. What are the number of possible arrangements?

• A. $5040$
• B. $720$
• C. $4005$
• D. None of the above

Answer 1

The correct option is A $5040$

Arrangement of $4$ balls out of $10$ different balls is similar to filling of $4$ vacant places using $10$ different things.


First place can be filled in $10$ possible ways.

Second can be filled in $9$ ways by using remaining $9$ balls.

Third and fourth place can be filled in $8$ and $7$ number of ways respectively.

Hence, all the arrangements of $4$ balls will be filling of first "and" second "and" third "and" fourth place.

So, total number of ways are $10\times 9\times 8\times 7=5040.$