Answer:
5040 ways
Explanation:
If we want to chose 4 people out of a group of 10 people.
Method 1
• We can choose the first person in 10 ways.
,• We can choose the second person in 9 ways.
,• We can choose the third person in 8 ways.
,• We can choose the fourth person in 7 ways.
Therefore, the number of ways this can be done is:
[tex]\begin{gathered} =10\times9\times8\times7 \\ =5040\text{ ways} \end{gathered}[/tex]Method 2
We can solve this as a combination problem.
[tex]\begin{gathered} \text{Number of ways=}^{10}C_4 \\ =\frac{10!}{(10-4)!} \\ =\frac{10\times9\times8\times7\times6!}{6!} \\ =10\times9\times8\times7 \\ =5040\text{ ways} \end{gathered}[/tex]Therefore, the selection can be done in 5040 ways.
