Question

Number of ways in which 9 different prizes can be given to 5 students, if one particular student receives 4 prizes and the rest of the students can get any numbers of prizes is:

• A. ${}^9{C}_4\cdot 2^{10}$
• B. ${}^9{C}_5\cdot 5^4$
• C. $4\cdot 4^5$
• D. None of these

Answer 1

The correct option is A ${}^9{C}_4\cdot 2^{10}$

Considering one student, giving him 4 prizes out of 9, is equal to choosing 4 things out of 9.

That can be done in
${}^9{C}_4$ ...(i)

We are left with 5 prizes. Distributing it to remaining 4 students can be done in$=4^5$ $=2^{10}ways.$ ...(ii)

Hence the required permutations will be ${}^9{C}_4\cdot 2^{10}$.