Task 3

 Part III

1.    Ahmed has started his own company. He plans to hire 8 new employees. He wants to hire males and females, knowing that there are an equal number of males and females applying for the job, use the binomial theorem to find the all combinations of males and females that could be hired.

Total :8,   (m+f)⁸

 = 8C₀ m⁸  + 8C₁ m⁷f¹  + 8C₂ m⁶f² + 8C₃ m⁵f³ + 8C₄ m⁴f⁴  + 8C₅ m³f⁵ + 8C₆ m²f⁶ + 8C₇ m¹f⁷ + 8C₈ f⁸ 

 = m⁸   + 8m⁷f + 28m⁶f² + 56m⁵f³ + 70m⁴f⁴ + 56m³f⁵ + 28m²f⁶ + 8mf⁷ +  f⁸

The number of all combinations of males and females 70m⁴f⁴

      

2.    Ahmed established a phone chain in which every staff member calls two other staff member to notify them about company events, the first round of calls begins with Ahmed calling two members. If there are 94 total staff members, how many rounds of calls are there to pass the information to all employees?

So, it will be between 7 or 8 rounds.

3.    Those employees will be seated around tables attached end-to-end for an event, How many tables are required to seat all the employees?