Answer:
So, we can do it in 720 ways.
Step-by-step explanation:
We have been given total of six trophies to arrange in the top shelf of the bookcase
If we need to arrange n things in different ways we can do it in n! ways
Similarly, Here we will do it in 6! ways
n!=n(n-1)(n-2).....1
So, 6!=6 x 5 x 4 x 3 x 2 x 1=720
The formula for N choose K is given as:
C(n, k)= ![\frac{n!}{[k!(n-k)!] }](https://tex.z-dn.net/?f=%20%5Cfrac%7Bn%21%7D%7B%5Bk%21%28n-k%29%21%5D%20%20%7D)
Where,
n is the total numbers.
k is the number of the selected item.
Options C is correct.
Dillion has 4 blue marbles and 12 red marbles
And max has 96 red marbles
Givens
Let the number of students in the class be x
Let the number of pieces of gum she gave out be 3x
Equation
3x + 8 = 168 This will not work out evenly. Let's try x - 1. The reason for that is because she may not give out anything to herself.
3(x - 1) + 8 = 168 This doesn't work either.
Well we have to choose. It's a rounding problem.
3x + 8 = 168 Subtract 8 from both sides.
3x = 168 - 8 Combine
3x = 160 Divide by 3 on both sides.
x = 160 / 3
x = 53.333333333
Since that can't be, we could say there were 53 students.
3x
The solution (-4,2) satisfies for the system of linear equations 3x + 13y = 14; 6x + 11y = -2
<u>Step-by-step explanation:</u>
Step 1:
Given detail is the solution of the equations (-4, 2) ie, x= - 4 and y = 2
This implies that this solution should satisfy the given linear equations.
Step 2:
Substitute values of x and y in the equations and verify whether the right hand side equals the left hand side.
System 1 Eq(1) ⇒ LHS = 3(-4) + 13 (2) = -12 + 26 = 14 = RHS
System 1 Eq(2) ⇒ LHS = 6(-4) + 11(2) = -24 + 22 = -2 = RHS
Therefore, the first system of linear equations satisfy the condition.