Kamal, Lalman, Manish, Nishant, Praveen, Qadir, Raman, Sanjay, Umang and Waqar 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.

(i) A team must include exactly one among Praveen, Raman, and Sanjay.

(ii) A team must include either Manish or Qadir, but not both.

(iii) If a team includes Kamal, then it must also include Lalman, and vice versa.

(iv) If a team include one among Sanjay, Umang, and Waqar, then it must also include the other two.

(v) Lalman and Nishant cannot be members of the same team. Lalman and Umang cannot be members of the same team.

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

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

Option 1 -

Option 2 -

Option 3 -

Option 4 -

1 View | Posted 3 months ago

Asked by Shiksha User

1 Answer

Answered by

Payal Gupta | Contributor-Level 10

3 months ago

Correct Option - 4

Detailed Solution:

If the team includes Nishant, then it does not include Lalman and Kamal.

Once out of Manish and Qadir can be include and one out of Praveen, Sanjay and Raman can be included. If Sanjay is a member, So we can select one out of Manish and Qadir in 2 ways

And we can select one out of Praveen, Sanjay and Raman in 3 ways

Hence total number of ways = 2 * 3 = 6 ways

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