Q26. 
A box contains $10$ balls out of which $3$ are red and rest are blue. In how many ways can a random sample of $6$ balls be drawn from the bag so that at the most $2$ red balls are included in the sample and no sample has all the $6$ balls of the same colour? 
A.  $105$ 

B.  $168$ 

C.  $189$ 

D.  $120$ 
Q27. 
Out of eight crew members three particular members can sit only on the left side. Another two particular members can sit only on the right side. Find the number of ways in which the crew can be arranged so that four men can sit on each side. 
A.  $864$ 

B.  $863$ 

C.  $865$ 

D.  $1728$ 
Q28. 
A man positioned at the origin of the coordinate system. the man can take steps of unit measure in the direction North, East, West or South. Find the number of ways of he can reach the point $(5,6)$, covering the shortest possible distance. 
A.  252 

B.  432 

C.  462 

D.  504 
Q29. 
There are $6$ equally spaced points $A,B,C,D,E$ and $F$ marked on a circle with radius $R$. How many convex pentagons of distinctly different areas can be drawn using these points as vertices? 
A.  ${^6P_5}$ 

B.  $1$ 

C.  $5$ 

D.  $\text{None of these}$ 
Q30. 
In an examination paper, there are two groups each containing $4$ questions. A candidate is required to attempt $5$ questions but not more than $3$ questions from any group. In how many ways can $5$ questions be selected? 
A.  24 

B.  48 

C.  96 

D.  64 