Q6. 
A college has $10$ basketball players. A $5$member team and a captain will be selected out of these $10$ players. How many different selections can be made? 
A.  $1260$ 

B.  $210$ 

C.  ${^{10}C_6} × 6!$ 

D.  ${^{10}C_5} × 6$ 
Q7. 
A $6\times 6$ grid is cut from an $8\times 8$ chessboard. In how many ways can we put two identical coins, one on the black square and one on a white square on the grid, such that they are not placed in the same row or in the same column? 
A.  216 

B.  324 

C.  144 

D.  108 
Q8. 
How many four letter distinct initials can be formed using the alphabets of English language such that the last of the four words is always a consonant? 
A.  ${26^3} × 21$ 

B.  $26 × 25 × 24 × 21$ 

C.  $25 × 24 × 23 × 21$ 

D.  $\text{None of these}$ 
Q9. 
What is the total number of ways in which Dishu can distribute $9$ distinct gifts among his $8$ distinct girlfriends such that each of them gets at least one gift? 
A.  $72 × 8!$ 

B.  $144 × 8!$ 

C.  $36 × 8!$ 

D.  $9!$ 
Q10. 
How many number of times will the digit $7$ be written when listing the integers from $1$ to $1000$? 
A.  271 

B.  300 

C.  252 

D.  304 