Question

Number of ways in which $9$ different prizes be given to $5$ students if one particular boy receives $4$ prices 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

Answer 1

Answer: (A)

${}^9{C}_4\cdot 2^{10}$

One particular student gets $4$ prizes ${=}^9{C}_4$ ways.

All rest $5$ prizes can be distributed to $4$ student $=4\times 4\times 4\times 4\times 4=1024$

Hence, total wyas ${=}^9{C}_4\times 1024.$