Question

$10$ different pens and two different books are distributed randomly to $3$ students giving $4$ things to each. The probability that books go to different students is

• A. $\frac{5}{11}$
• B. $\frac{6}{11}$
• C. $\frac{7}{11}$
• D. $\frac{8}{11}$

Answer 1

The correct option is C $\frac{7}{11}$

$P$(book go to different students)$=1-P$ (book go to same student)

${\Rightarrow }^4{C}_1=4$ ways to choose which student gets both books.

The remaining objects can be distributed in ${}^{10}{C}_4{\times }^6{C}_4$ ways

Thus, the total favourable cases $=4{\times }^{10}{C}_4{\times }^6{C}_4$

Total possible ways to distribute 12 items ${=}^{12}{C}_4{\times }^8{C}_4$

Thus, $P$ (both book go to same student) ${}^{12}{C}_4{\times }^8{C}_4$

$\therefore$ Required probability $=1-\frac{4}{11}=\frac{7}{11}$