Respuesta :
Answer:
A. 6
Step-by-step explanation:
Let n represent number of tables.
We have been given that to furnish a room in a model home, an interior decorator is to select 2 chairs and 2 tables from a collection of chairs and tables in a warehouse that are all different from each other. There are 5 chairs in the warehouse and if 150 different combinations are possible.
Since 2 chairs are being selected from 5 chairs, so we can choose 2 chairs in [tex]5C2[/tex] ways.
There are n tables and we can choose 2 tables from n table in [tex]nC2[/tex] ways.
We can represent our given information in an equation as:
[tex]5C2\times nC2=150[/tex]
[tex]\frac{5!}{2!(5-2)!}\times \frac{n!}{2!(n-2)!}=150[/tex]
[tex]\frac{5*4*3!}{2*1*3!}\times \frac{n!}{2!(n-2)!}=150[/tex]
[tex]10\times \frac{n!}{2!(n-2)!}=150[/tex]
[tex]\frac{n!}{2!(n-2)!}=15[/tex]
[tex]\frac{n!}{2*1*(n-2)!}=15[/tex]
[tex]\frac{n*(n-1)*(n-2)!}{2*(n-2)!}=15[/tex]
[tex]\frac{n(n-1)}{2}=15[/tex]
[tex]n(n-1)=30[/tex]
[tex]n^2-n=30[/tex]
[tex]n^2-n-30=0[/tex]
[tex]n^2-6n+5n-30=0[/tex]
[tex]n(n-6)+5(n-6)=0[/tex]
[tex](n-6)(n+5)=0[/tex]
[tex](n-6)=0\text{ (or) }(n+5)=0[/tex]
[tex]n=6\text{ (or) }n=-5[/tex]
Since tables cannot be negative quantity, therefore, 6 tables are in the warehouse.
