Respuesta :
Answer: 66 ways
Step-by-step explanation:
Given;
Number of senior math club members = 6
Number of junior math club members = 4
Total number of members of the club = 10
To form a group of 5 members with at least 4 seniors.
N = Na + Nb
Na = number of possible ways of selecting 4 seniors and 1 junior
Nb = number of possible ways of selecting 5 seniors.
Since the selection is does not involve ranks(order is not important)
Na = 6C4 × 4C1 = 6!/4!2! × 4!/3!1! = 15 ×4 = 60
Nb = 6C5 = 6!/5!1! = 6
N = Na + Nb = 60+6
N = 66 ways
Using the combination formula, it is found that there are 66 ways to form the groups.
The order in which the students are selected is not important, hence, the combination formula is used to solve this question.
What is the combination formula?
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, the possible groups are:
- One junior from a set of 4 and 4 seniors from a set of 6.
- 5 seniors from a set of 6.
Hence:
[tex]T = C_{4,1}C_{6,4} + C_{6,5} = \frac{4!}{1!3!}\frac{6!}{4!2!} + \frac{6!}{5!1!} = 4(15) + 6 = 60 + 6 = 66[/tex]
There are 66 ways to form the groups.
You can learn more about the combination formula at https://brainly.com/question/25821700
