Q11. 
In how many ways can $15$ people be seated around two round tables with seating capacities of $7$ and $8$ people? 
A.  $\dfrac{15!}{8!}$ 

B.  $7!×8!$ 

C.  ${^{15}C_8}×6!×7!$ 

D.  $2×{^{15}C_7}×6!×7!$ 

E.  ${^{15}C_8} × 8!$ 
Q12. 
In how many ways can the letters of the word $EDUCATION$ be rearranged so that the relative position of the vowels and consonants remain the same as in the word $EDUCATION$? 
A.  $\dfrac{9!}{4}$ 

B.  $\dfrac{9!}{4! × 5!}$ 

C.  $4! × 5!$ 

D.  $\text{None of these}$ 
Q13. 
A committee is to be formed comprising $7$ members such that there is a simple majority of men and at least $1$ woman. The shortlist consists of $9$ men and $6$ women. In how many ways can this committee be formed? 
A.  $3,724$ 

B.  $3,630$ 

C.  $4,914$ 

D.  $3,824$ 
Q14. 
A team of $8$ students goes on an excursion, in two cars, of which one can seat $5$ and the other only $4$. In how many ways can they travel? 
A.  9 

B.  26 

C.  126 

D.  392 
Q15. 
A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims $10$ cups of tea are prepared, $5$ in one way and $5$ in other. Find the different possible ways of presenting these $10$ cups to the expert. 
A.  252 

B.  240 

C.  300 

D.  340 