Question

Evaluate.
5 P 3 x 6 C 4

a. 150
b. 300
c. 900

Answer 1

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 2

Option (c) is correct.

`^5P_3*^6C_4` is 900

Explanation:

Given :Expression
`^5P_3*^6C_4`

We have to find the value of given expression
`^5P_3*^6C_4`

Consider the given expression
`^5P_3*^6C_4`

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

`nPr=(n!)/(\left(n-r\right)!)`

and The number of subset of r elements from n elements
`nCr=(n!)/(r!\left(n-r\right)!)`

Thus,
`^5P_3=(5!)/(\left(5-3\right)!)==(5!)/(2!)=5\cdot \:4\cdot \:3=60`

and
`^6C_4=(6!)/(4!\left(6-4\right)!)==(6!)/(4!\cdot \:2!)==(6\cdot \:5)/(2!)=15`

Thus,
`^5P_3*^6C_4=60* 15=900`

Thus,
`^5P_3*^6C_4` is 900