Arranging a 6-member Committee?

📌 CONCEPT: The concept of arranging a group of people (in this case, a 6-member committee) such that certain conditions are met (no two boys are seated together) is a classic example of a permutation problem with a restriction.

📐 RULE / FORMULA: The formula for permutations with a restriction is given by nPr, where n is the total number of people and r is the number of people being arranged, multiplied by the number of ways the restriction can be satisfied.

💡 WORKED EXAMPLE: Let's consider arranging the 6-member committee with 3 boys and 3 girls such that no two boys are seated together. We first arrange the 3 girls in 3! = 6 ways. Then, we arrange the 3 boys in the 5 remaining seats in 5P3 = 5 × 4 × 3 = 60 ways. Therefore, the total number of ways to arrange the committee is 6 × 60 = 360.

⚠️ COMMON MISTAKE: Students often forget to consider the restriction and calculate the total number of permutations without accounting for the condition, leading to an incorrect answer.