Question

Evaluate. 5 P 3 x 6 C 4 a. 150 b. 300 c. 900

Answer 1

Answer:

Option (c) is correct.

$^5P_3\times^6C_4$  is 900

Step-by-step explanation:

 Given  :Expression  $^5P_3\times^6C_4$      

We have to find the value of given expression $^5P_3\times^6C_4$  

Consider the given expression  $^5P_3\times^6C_4$        

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

$nPr=\frac{n!}{\left(n-r\right)!}$

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

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

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

Thus, $^5P_3\times^6C_4=60\times 15=900$    

Thus,  $^5P_3\times^6C_4$  is 900

Answer 2

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