Question

Number of ways in which $9$ different prizes be given to $5$ students if one particular boy receives $4$ prizes $\&$ 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. ${4.4}^5$
• D. none

Answer 1

The correct option is 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 $4$ students

$=4^{\ast }{4}^{\ast }{4}^{\ast }4$

$=1024$ ways

So total ways ${=}^9{C}_4\ast 1024$ ways.