There are
ways of picking 2 of the 10 available positions for a 0. 8 positions remain.
There are
ways of picking 3 of the 8 available positions for a 1. 5 positions remain, but we're filling all of them with 2s, and there's
way of doing that.
So we have
![\dbinom{10}2\dbinom83\dbinom55=\dfrac{10!}{2!(10-2)!}\dfrac{8!}{3!(8-3)!}\dfrac{5!}{5!(5-5)!}=2520](https://tex.z-dn.net/?f=%5Cdbinom%7B10%7D2%5Cdbinom83%5Cdbinom55%3D%5Cdfrac%7B10%21%7D%7B2%21%2810-2%29%21%7D%5Cdfrac%7B8%21%7D%7B3%21%288-3%29%21%7D%5Cdfrac%7B5%21%7D%7B5%21%285-5%29%21%7D%3D2520)
The last expression has a more compact form in terms of the so-called multinomial coefficient,
![\dbinom{10}{2,3,5}=\dfrac{10!}{2!3!5!}=2520](https://tex.z-dn.net/?f=%5Cdbinom%7B10%7D%7B2%2C3%2C5%7D%3D%5Cdfrac%7B10%21%7D%7B2%213%215%21%7D%3D2520)
Answer:
2! Thank it if it was helpful :D
Step-by-step explanation:
7x-4x=3+3
3x=6
x=2
Answer:
<em>x = 7</em>
Step-by-step explanation:
Simplifying
17 = 3X + -4
Reorder the terms:
17 = -4 + 3X
Solving
17 = -4 + 3X
Solving for variable 'X'.
Move all terms containing X to the left, all other terms to the right.
Add '-3X' to each side of the equation.
17 + -3X = -4 + 3X + -3X
Combine like terms: 3X + -3X = 0
17 + -3X = -4 + 0
17 + -3X = -4
Add '-17' to each side of the equation.
17 + -17 + -3X = -4 + -17
Combine like terms: 17 + -17 = 0
0 + -3X = -4 + -17
-3X = -4 + -17
Combine like terms: -4 + -17 = -21
-3X = -21
Divide each side by '-3'.
X = 7
Simplifying
X = 7
Answer:
-3.69
Step-by-step explanation:
Exponential equations can be solved by taking Ln (natural logarithm) of both sides. The rule we need to know is:
![Ln(a^b)=bLn(a)](https://tex.z-dn.net/?f=Ln%28a%5Eb%29%3DbLn%28a%29)
Now lets work out this problem:
![16^{2x+3}=13^{x-1}\\Ln(16^{2x+3})=Ln(13^{x-1})\\(2x+3)Ln(16)=(x-1)Ln(13)](https://tex.z-dn.net/?f=16%5E%7B2x%2B3%7D%3D13%5E%7Bx-1%7D%5C%5CLn%2816%5E%7B2x%2B3%7D%29%3DLn%2813%5E%7Bx-1%7D%29%5C%5C%282x%2B3%29Ln%2816%29%3D%28x-1%29Ln%2813%29)
Using calculator, we take the values of Ln 16 and Ln 13 as:
Ln 16 = 2.7726
Ln 13 = 2.5649
Now, we can solve for x:
![(2x+3)Ln(16)=(x-1)Ln(13)\\(2x+3)2.7726=(x-1)2.5649\\5.5452x+8.3178=2.5649x-2.5649\\2.9803x=-10.8827\\x=-3.69](https://tex.z-dn.net/?f=%282x%2B3%29Ln%2816%29%3D%28x-1%29Ln%2813%29%5C%5C%282x%2B3%292.7726%3D%28x-1%292.5649%5C%5C5.5452x%2B8.3178%3D2.5649x-2.5649%5C%5C2.9803x%3D-10.8827%5C%5Cx%3D-3.69)
x is -3.69 (rounded to 2 decimal places)
Answer:
What are you asking?
Step-by-step explanation: