Question

10 pens of different shape and size are to be distributed to 6 students at random. The probability that a particular student receives 4 pens is

• A. $\frac{10C_4}{10C_6}$
• B. $\frac{10C_4}{{10}^6}$
• C. $\frac{10C_4\times 5^6}{6^{10}}$
• D. $\frac{10C_4\times 5^6}{3^{10}}$

Answer 1

Answer: (C)

$\frac{10C_4\times 5^6}{6^{10}}$

Since the student is pre-decided, we choose the 4 pens that we want to give to him. $⟹{}^{10}{C}_4$
Now with the remaining 5 students and 6 pens , while distributing, each pen has 5 choices $⟹5^6$
and the universal set $⟹6^{10}$
Hence, the answer.