Answer: 2x1x3
Step-by-step explanation:
the formula for volume is LxWxH so if L=2 then 2x1x3= a volume of 6
Answer:
216
Step-by-step explanation:
Formula for permutation is:
![\boxed{ \tt^{n} C_{r} = \frac{n!}{r!(n - r)!} }](https://tex.z-dn.net/?f=%20%5Cboxed%7B%20%5Ctt%5E%7Bn%7D%20C_%7Br%7D%20%3D%20%20%5Cfrac%7Bn%21%7D%7Br%21%28n%20-%20r%29%21%7D%20%7D)
<h3><u>Calculation</u>, </h3>
Plug in the values:
Required number of ways = ²C7
![\sf \frac{7!}{5!(7 - 5)!}](https://tex.z-dn.net/?f=%20%5Csf%20%5Cfrac%7B7%21%7D%7B5%21%287%20-%205%29%21%7D%20)
![\sf \frac{7 \times 6 \times \cancel{5!}}{ \cancel{5! }\times 2!}](https://tex.z-dn.net/?f=%20%5Csf%20%5Cfrac%7B7%20%5Ctimes%206%20%5Ctimes%20%20%5Ccancel%7B5%21%7D%7D%7B%20%5Ccancel%7B5%21%20%7D%5Ctimes%202%21%7D%20)
![\sf \frac{7 \times 6 }{ 2!}](https://tex.z-dn.net/?f=%20%5Csf%20%5Cfrac%7B7%20%5Ctimes%206%20%7D%7B%202%21%7D%20)
![\sf \frac{42 }{ 2!}](https://tex.z-dn.net/?f=%20%5Csf%20%5Cfrac%7B42%20%7D%7B%202%21%7D%20)
![\sf \frac{42 }{ 2} = 21](https://tex.z-dn.net/?f=%20%5Csf%20%5Cfrac%7B42%20%7D%7B%202%7D%20%20%3D%2021)
<em>Thus, </em><em>The</em><em> </em><em>players</em><em> </em><em>can</em><em> </em><em>be</em><em> </em><em>selected</em><em> </em><em>in</em><em> </em><em>21</em><em> </em><em>different</em><em> </em><em>ways</em><em>!</em><em>!</em><em>~</em>
![\begin{cases}4x+2\ge14\\-21x+1](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D4x%2B2%5Cge14%5C%5C-21x%2B1%3C22%5Cend%7Bcases%7D)
In the first inequality, we have
![4x+2\ge14\implies4x\ge12\implies x\ge3](https://tex.z-dn.net/?f=4x%2B2%5Cge14%5Cimplies4x%5Cge12%5Cimplies%20x%5Cge3)
In the second, we have
![-21x+1](https://tex.z-dn.net/?f=-21x%2B1%3C22%5Cimplies-21x%3C21%5Cimplies%20x%3E-1)
The solution to the system is the intersection of these two intervals, which would be
.