Q21. 
How many 5digit positive integers exist the sum of whose digits are odd? 
A.  $36,000$ 

B.  $38,000$ 

C.  $45,000$ 

D.  $90,000$ 
Q22. 
There are eight boxes of chocolates, each box containing distinct number of chocolates from 1 to 8. In how many ways four of these boxes can be given to four persons (one boxes to each) such that the first person gets more chocolates than each of the three, the second person gets more chocolates than the third as well as the fourth persons and the third person gets more chocolates than fourth person? 
A.  35 

B.  70 

C.  105 

D.  210 
Q23. 
In how many ways can seven friends be seated in a row having 35 seats, such that no two friends occupy adjacent seats? 
A.  ${^{29}P_7}$ 

B.  ${^{29}C_7}$ 

C.  ${^{28}P_7}$ 

D.  ${^{29}C_7}$ 
Q24. 
How many ways can 10 letters be posted in 5 post boxes, if each of the post boxes can take more than 10 letters? 
A.  $5^{10}$ 

B.  ${10}^5$ 

C.  ${^{10}P_5}$ 

D.  ${^{10}C_5}$ 
Q25. 
There are 2 brothers among a group of 20 persons. In how many ways can the group be arranged around a circle so that there is exactly one person between the two brothers? 
A.  2 × 17! 

B.  18! × 18 

C.  19! × 18 

D.  2 × 18! 

E.  2 × 17! × 17! 