### CAT 2006 Question Paper Question 47

Instructions

K, L, M, N, P, Q, R, S, U and W are the only ten members in a department. There is a proposal to form a team from within the members of the department, subject to the following conditions:

1.  A team must include exactly one among P,R and S.
2.  A team must include either M or Q, but not both.
3.  If a team includes K, then it must also include L, and vice versa.
4.  If a team includes one among S, U and W, then it should also include the other two.
5.  L and N cannot be members of the same team.
6.  L and U cannot be members of the same team.

The size of a team is defined as the number of members in the team.

Question 47

# In how many ways a team can be constituted so that the team includes N?

Solution

Since N is in the team, L and K cannot be in the team.
The team can have one of M and Q. So, 2 ways of selection.
If the team has S, then it should have U and W as well.
If the team has no S, then it should have one of P or R.
So, the number of ways of forming the team is 2*(1+2) = 6 ways

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