Respuesta :

The answer is 300 because if u x the 5x3=15 and divide 6 and 4 is 1.5 then multipy that 22 then you put the letters in the equations

Answer:

Option (c) is correct.

[tex]^5P_3\times^6C_4[/tex]  is 900

Step-by-step explanation:

 Given  :Expression  [tex]^5P_3\times^6C_4[/tex]      

We have to find the value of given expression [tex]^5P_3\times^6C_4[/tex]  

Consider the given expression  [tex]^5P_3\times^6C_4[/tex]        

The possibility of choosing an ordered set of r object from n object is given by  

[tex]nPr=\frac{n!}{\left(n-r\right)!}[/tex]

and The number of subset of r elements from n elements           [tex]nCr=\frac{n!}{r!\left(n-r\right)!}[/tex]        

Thus, [tex]^5P_3=\frac{5!}{\left(5-3\right)!}==\frac{5!}{2!}=5\cdot \:4\cdot \:3=60[/tex]

and [tex]^6C_4=\frac{6!}{4!\left(6-4\right)!}==\frac{6!}{4!\cdot \:2!}==\frac{6\cdot \:5}{2!}=15[/tex]

Thus, [tex]^5P_3\times^6C_4=60\times 15=900[/tex]    

Thus,  [tex]^5P_3\times^6C_4[/tex]  is 900