You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.
So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:
C (m,n) = m! / (n! * (m -n)! )
=> C (50,30) = 50! / (30! (50 - 30)! ) = (50!) / [30! (50 - 30)!] = 50! / [30! 20!] =
= 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.
Answer:
100y - 16
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
x+(x+1)+(x+2)= 48
=)3x+3=48
=)3x=45
X=15
we can simply pick any two points off the x,y table, so
![\bf \begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} 0&20\\ 3&11\\ 6&2\\ 9&-7\\ \cline{1-2} \end{array} \begin{array}{llll} \\[1em] \leftarrow \textit{let's use this point}\\\\ \leftarrow \textit{and this point} \end{array}~\hspace{5em} (\stackrel{x_1}{3}~,~\stackrel{y_1}{11})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{-7}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-7-11}{9-3}\implies \cfrac{-18}{6}\implies -3](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7B%7Ccc%7Cll%7D%0A%5Ccline%7B1-2%7D%0Ax%26y%5C%5C%0A%5Ccline%7B1-2%7D%0A0%2620%5C%5C%0A3%2611%5C%5C%0A6%262%5C%5C%0A9%26-7%5C%5C%0A%5Ccline%7B1-2%7D%0A%5Cend%7Barray%7D%0A%5Cbegin%7Barray%7D%7Bllll%7D%0A%5C%5C%5B1em%5D%0A%5Cleftarrow%20%5Ctextit%7Blet%27s%20use%20this%20point%7D%5C%5C%5C%5C%0A%5Cleftarrow%20%5Ctextit%7Band%20this%20point%7D%0A%5Cend%7Barray%7D~%5Chspace%7B5em%7D%0A%28%5Cstackrel%7Bx_1%7D%7B3%7D~%2C~%5Cstackrel%7By_1%7D%7B11%7D%29%5Cqquad%0A%28%5Cstackrel%7Bx_2%7D%7B9%7D~%2C~%5Cstackrel%7By_2%7D%7B-7%7D%29%0A%5C%5C%5C%5C%5C%5C%0Aslope%20%3D%20m%5Cimplies%0A%5Ccfrac%7B%5Cstackrel%7Brise%7D%7B%20y_2-%20y_1%7D%7D%7B%5Cstackrel%7Brun%7D%7B%20x_2-%20x_1%7D%7D%5Cimplies%20%5Ccfrac%7B-7-11%7D%7B9-3%7D%5Cimplies%20%5Ccfrac%7B-18%7D%7B6%7D%5Cimplies%20-3)
