Respuesta :
Answer:
1) 24
2)66
Explanation:
1) How many different ways can you arrange four people in four numbered chairs?
Answer: we have 4 people ands 4 chairs, so we use the factorial of 4 to find the number of ways that we can arrenge the people:
[tex]4!\text{ = 4}\cdot3\cdot2\cdot1=24[/tex]we can arrange 4 people in 4 chairs in 24 different ways
2)How many ways can you distribute 10 balloons to 3 children?
To distribute "n" objects to "r" people (in this case n=10, and r = 3) we use the following combinarions formula:
[tex]C(n+r-1,r-1)[/tex]substituting our values we get:
[tex]C(10+3-1,3-1)[/tex][tex]C(12,2)[/tex]and since C(a,b) is defined as:
[tex]C(a,b)=\frac{a!}{b!(a-b)!}[/tex]For C(12,2) we get the following:
[tex]C(12,2)=\frac{12!}{2!(12-2)!}[/tex]which simplifies to:
[tex]C(12,2)=\frac{12!}{2!(10)!}=66[/tex]We can distribute 10 balloons to 3 people in 66 ways
