Arranging Committee Members?

📌 CONCEPT: The problem involves forming a committee of 4 members from a group of 7, with a specific condition that Mr. Kumar must be included and also select 2 of his classmates.

📐 RULE / FORMULA: To solve this, we can use the combination formula, nCr = n! / (r!(n-r)!), where n is the total number of members and r is the number of members to be selected, in this case, 7C3 or 7C4.

💡 WORKED EXAMPLE: Suppose we have 7 members: A, B, C, D, E, F, and G. Mr. Kumar insists on being part of the committee. We need to select 2 more classmates to complete the committee of 4. First, we choose 2 from the 6 non-Mr. Kumar members. The number of ways to choose 2 from 6 is 6C2 = 6! / (2! * (6-2)!) = 15. Next, we need to arrange these 4 members in a committee of 4, which is 4! = 24. Therefore, the total number of different committees that can be formed is 15 * 24 = 360.

⚠️ COMMON MISTAKE: Students often forget to consider the condition of Mr. Kumar being included and also selecting 2 of his classmates, which leads to incorrect application of the combination formula.