[tex]\mathbb{SOLUTION:}[/tex]
According to the problem is on how a group of 4 people can be created from a group of 6 people.
Using the combination formula to determine the answer of how many ways can we create a group of 4 peope into a 6 people.
[tex]\begin{gathered}\begin{aligned} & \bold{Formula:} \\ & \quad \boxed{\begin{array}{l} \large\rm{C = \frac{n!}{(n−r)!r!}} \end{array}}\, \\ \end{aligned} \end{gathered}[/tex]
- [tex]\begin{gathered} \rm{C} = \frac{6!}{(6 - 4)!4!}\end{gathered}[/tex]
- [tex]\begin{gathered} \rm{C} = \frac{6!}{(2)!4!} \end{gathered}[/tex]
- [tex]\begin{gathered} \rm{C} = \frac{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 }{(2 \cdot 1)4 \cdot 3 \cdot 2 \cdot 1} \end{gathered}[/tex]
- [tex]\begin{gathered} \rm{C} = \frac{6 \cdot 5 \cdot 4 \cdot 3}{4 \cdot 3 \cdot 2 \cdot 1} \end{gathered}[/tex]
- [tex]\begin{gathered} \rm{C} = \frac{360}{24} \end{gathered}[/tex]
- [tex]\begin{gathered} \rm{C} = 15 \end{gathered}[/tex]
Hence, 15 ways can we create a group
Answer : [tex]\boxed{\rm C = 15}[/tex]
