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In how many ways can we create a group of 4 peope from 6 people , a.360, b.30, c.15, d.12

By CindyPosted on June 13, 2022

In how many ways can we create a group of 4 peope from 6 people

a.360
b.30
c.15
d.12

$\mathbb{SOLUTION:}$

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.

$\begin{gathered}\begin{aligned} & \bold{Formula:} \\ & \quad \boxed{\begin{array}{l} \large\rm{C = \frac{n!}{(n−r)!r!}} \end{array}}\, \\ \end{aligned} \end{gathered}$

$\begin{gathered} \rm{C} = \frac{6!}{(6 - 4)!4!}\end{gathered}$

$\begin{gathered} \rm{C} = \frac{6!}{(2)!4!} \end{gathered}$

$\begin{gathered} \rm{C} = \frac{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 }{(2 \cdot 1)4 \cdot 3 \cdot 2 \cdot 1} \end{gathered}$

$\begin{gathered} \rm{C} = \frac{6 \cdot 5 \cdot 4 \cdot 3}{4 \cdot 3 \cdot 2 \cdot 1} \end{gathered}$

$\begin{gathered} \rm{C} = \frac{360}{24} \end{gathered}$

$\begin{gathered} \rm{C} = 15 \end{gathered}$

Hence, 15 ways can we create a group

Answer : $\boxed{\rm C = 15}$

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