There are 142506 ways in which 5 students can be selected out of 30 students.
<h3>How can a certain number of individuals be selected using a combination?</h3>
The selection of 5 students out of 30 students can be achieved with the use of combination since the order of selection is not required to be put into consideration.
By using the formula:
![\mathbf{^nC_r = \dfrac{n!}{r!(n-r)!}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5EnC_r%20%3D%20%5Cdfrac%7Bn%21%7D%7Br%21%28n-r%29%21%7D%7D)
where;
- n = total number of individual in the set = 30
- r = number of chosing individuals to be selected = 5
![\mathbf{^nC_r = \dfrac{30!}{5!(30-5)!}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5EnC_r%20%3D%20%5Cdfrac%7B30%21%7D%7B5%21%2830-5%29%21%7D%7D)
![\mathbf{^nC_r = \dfrac{30!}{5!(25)!}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5EnC_r%20%3D%20%5Cdfrac%7B30%21%7D%7B5%21%2825%29%21%7D%7D)
![\mathbf{^nC_r = 142506}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5EnC_r%20%3D%20142506%7D)
Learn more about combination here:
brainly.com/question/11732255
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Answer:
Yes, since log(2) and log(5) both exist as valid values for the logarithm.
didnt check if ur equation is correct though
Answer:
Sounds like Sam better pull it together
Step-by-step explanation:
Answer:
c S(x) = 12(3,000) + 0.025(x – 250,000)
Step-by-step explanation:
I got it right
Step-by-step explanation:
Let assume that
Cost of 1 burger = $ x
Cost of 1 doughnuts = $ y
According to statement, 9 burgers and 1 doughnut cost $ 31.30
![\begin{gathered}\sf \: 9x + y = 31.3 \\ \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Csf%20%5C%3A%209x%20%2B%20y%20%3D%2031.3%20%5C%5C%20%5C%5C%20%5Cend%7Bgathered%7D)
![\begin{gathered}\sf\implies \sf \: y = 31.3 - 9x - - - (1) \\ \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Csf%5Cimplies%20%5Csf%20%5C%3A%20y%20%3D%2031.3%20-%209x%20-%20-%20-%20%281%29%20%5C%5C%20%5C%5C%20%5Cend%7Bgathered%7D)
According to statement again, 3 doughnuts and 6 burgers cost $ 26.70
![\begin{gathered}\sf \: 6x + 3y = 26.7 \\ \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Csf%20%5C%3A%206x%20%2B%203y%20%3D%2026.7%20%5C%5C%20%5C%5C%20%5Cend%7Bgathered%7D)
![\begin{gathered}\sf \: 3(2x + y) = 26.7 \\ \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Csf%20%5C%3A%203%282x%20%2B%20y%29%20%3D%2026.7%20%5C%5C%20%5C%5C%20%5Cend%7Bgathered%7D)
![\begin{gathered}\sf \: 2x + y = 8.9 \\ \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Csf%20%5C%3A%202x%20%2B%20y%20%3D%208.9%20%5C%5C%20%5C%5C%20%5Cend%7Bgathered%7D)
On substituting the value of y from equation (1), we get
![\begin{gathered}\sf \: 2x + 31.3 - 9x = 8.9 \\ \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Csf%20%5C%3A%202x%20%2B%2031.3%20-%209x%20%3D%208.9%20%5C%5C%20%5C%5C%20%5Cend%7Bgathered%7D)
![\begin{gathered}\sf \: 31.3 - 7x = 8.9 \\ \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Csf%20%5C%3A%2031.3%20-%207x%20%3D%208.9%20%5C%5C%20%5C%5C%20%5Cend%7Bgathered%7D)
![\begin{gathered}\sf \: - 7x = 8.9 - 31.3 \\ \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Csf%20%5C%3A%20-%207x%20%3D%208.9%20-%2031.3%20%5C%5C%20%5C%5C%20%5Cend%7Bgathered%7D)
![\begin{gathered}\sf \: - 7x = - 22.4 \\ \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Csf%20%5C%3A%20-%207x%20%3D%20-%2022.4%20%5C%5C%20%5C%5C%20%5Cend%7Bgathered%7D)
![\begin{gathered}\bf\implies \: x = 3.2 \\ \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Cbf%5Cimplies%20%5C%3A%20x%20%3D%203.2%20%5C%5C%20%5C%5C%20%5Cend%7Bgathered%7D)
So,
Cost of 2 burgers = 3.2 × 2 = <u>$ 6.4</u>