Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • A committee of 6 members needs to be formed from a group of 12 professionals. However, two specific professionals, Michael and Lisa, cannot be on the committee together.

A committee of 6 members needs to be formed from a group of 12 professionals. However, two specific professionals, Michael and Lisa, cannot be on the committee together. In how many ways can the committee be formed?

Option: 1

504


Option: 2

100


Option: 3

126


Option: 4

200


Answers (1)

best_answer

Number of professionals = 12

Number of professionals to be selected = 6

Number of ways to select 6 professionals from 12 without Michael and Lisa together:

Selecting Michael:

We need to select 5 more professionals from the remaining 10 (excluding Michael and Lisa). This can be done in \mathrm{C(10,5)}ways.

Selecting Lisa:

Similarly, we need to select 5 more professionals from the remaining 10 (excluding Michael and Lisa). This can also be done in \mathrm{C(10,5)}ways.

\mathrm{\text { Total number of ways }=C(10,5)+C(10,5)=252+252=504 \text { ways. } }

Therefore, the team can be formed in 56 ways, and the committee can be formed in 504 ways.

Hence option 1 is correct.

Posted by

Rakesh

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2026 session 2 application correction begins on jeemain.nta.nic.in; edit details by tomorrow
anam-khan

JEE Main 2026 Registration LIVE: Session 2 exam from April 2 to 9; shift timings, admit card, exam pattern
anam-khan

JEE Main 2026 session 2 registration ends today for BTech, BArch; apply at jeemain.nta.nic.in

Latest Question