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