Question

2. a. The center for research in data science has a vacancy of 5 interns under a research attachment program. However, 20 students have applied. Determine the number of ways to select a team of 5 interns given that all students fulfill the minimum CGPA criteria. [3 marks]

Answer 1

Answer:  15504

Step-by-step explanation:

Given : The center for research in data science has a vacancy of 5 interns under a research attachment program.

Number of students applied = 20

The combination of n people taking r at a time is given by :-

$C(n,r)=\dfrac{n!}{r!(n-r)!}$

Since, all students fulfill the minimum CGPA criteria it means all 20 students are equally eligible.

Then , the number of ways to select a team of 5 interns from all 20 interns :-

$C(20,5)=\dfrac{20!}{5!(20-5)!}\\\\=\dfrac{20\times19\times18\times17\times16\times15!}{5!15!}\\\\=15504$

Hence, the number of ways to select a team of 5 interns. =