Respuesta :
Answer:
The number of tables in the warehouse are:
6
Step-by-step explanation:
We know that the method of combination is used to find the number of combinations possible in order to select r items from a set of n items
and is given by:
[tex]n_C_r=\dfrac{n!}{r!\times (n-r)!}[/tex]
Now, it is given that:
In order to furnish a room we have to select 2 chairs and 2 tables from 5 chairs and let there are t tables.
Also, the total number of combinations possible are: 150
i.e.
[tex]5_C_2\times t_C_2=150\\\\i.e.\\\\\dfrac{5!}{2!\times (5-2)!}\times \dfrac{t!}{2!\times (t-2)!}=150\\\\\dfrac{5!}{2!\times 3!}\times \dfrac{t(t-1)(t-2)!}{2\times (t-2)!}=150\\\\10\times \dfrac{t(t-1)}{2}=150\\\\5t(t-1)=150\\\\t(t-1)=30\\\\t^2-t-30=0\\\\t^2-6t+5t-30=0\\\\t(t-6)+5(t-6)=0\\\\(t+5)(t-6)=0\\\\i.e.\\\\t=-5\ or\ t=6[/tex]
But the number of table can't be negative.
Hence, we get:
[tex]t=6[/tex]
There are 6 tables in the warehouse.
