Option C
2100 different committees that can be formed from 5 teachers and 10 students
<em><u>Solution:</u></em>
A school committee consists of 2 teachers and 4 students
The number of different committees that can be formed from 5 teachers and 10 students is to be found
This is a combination problem
A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected
<em><u>The formula to calculate combinations is:</u></em>
![n C_{r}=\frac{n !}{r !(n-r) !}](https://tex.z-dn.net/?f=n%20C_%7Br%7D%3D%5Cfrac%7Bn%20%21%7D%7Br%20%21%28n-r%29%20%21%7D)
where n represents the number of items, and r represents the number of items being chosen at a time
Here we have to choose 2 teacher from 5 teacher and 4 student from 10 student
Hence we get,
Number of committees = ![5C_2 \times 10C_4](https://tex.z-dn.net/?f=5C_2%20%5Ctimes%2010C_4)
![\begin{aligned}&5 C_{2} \times 10 C_{4}=\frac{5 !}{2 !(5-2) !} \times \frac{10 !}{4 !(10-4) !}\\\\&5 C_{2} \times 10 C_{4}=\frac{5 !}{2 ! \times 3 !} \times \frac{10 !}{4 ! \times 6 !}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%265%20C_%7B2%7D%20%5Ctimes%2010%20C_%7B4%7D%3D%5Cfrac%7B5%20%21%7D%7B2%20%21%285-2%29%20%21%7D%20%5Ctimes%20%5Cfrac%7B10%20%21%7D%7B4%20%21%2810-4%29%20%21%7D%5C%5C%5C%5C%265%20C_%7B2%7D%20%5Ctimes%2010%20C_%7B4%7D%3D%5Cfrac%7B5%20%21%7D%7B2%20%21%20%5Ctimes%203%20%21%7D%20%5Ctimes%20%5Cfrac%7B10%20%21%7D%7B4%20%21%20%5Ctimes%206%20%21%7D%5Cend%7Baligned%7D)
To get the factorial of a number n the given formula is used,
![n !=n \times(n-1) \times(n-2) \ldots \times 2 \times 1](https://tex.z-dn.net/?f=n%20%21%3Dn%20%5Ctimes%28n-1%29%20%5Ctimes%28n-2%29%20%5Cldots%20%5Ctimes%202%20%5Ctimes%201)
Therefore,
![5 C_{2} \times 10 C_{4}=\frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1 \times 3 \times 2 \times 1} \times \frac{10 \times 9 \times \ldots . \times 2 \times 1}{4 \times 3 \times 2 \times 1 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}](https://tex.z-dn.net/?f=5%20C_%7B2%7D%20%5Ctimes%2010%20C_%7B4%7D%3D%5Cfrac%7B5%20%5Ctimes%204%20%5Ctimes%203%20%5Ctimes%202%20%5Ctimes%201%7D%7B2%20%5Ctimes%201%20%5Ctimes%203%20%5Ctimes%202%20%5Ctimes%201%7D%20%5Ctimes%20%5Cfrac%7B10%20%5Ctimes%209%20%5Ctimes%20%5Cldots%20.%20%5Ctimes%202%20%5Ctimes%201%7D%7B4%20%5Ctimes%203%20%5Ctimes%202%20%5Ctimes%201%20%5Ctimes%206%20%5Ctimes%205%20%5Ctimes%204%20%5Ctimes%203%20%5Ctimes%202%20%5Ctimes%201%7D)
![5 C_{2} \times 10 C_{4}=2100](https://tex.z-dn.net/?f=5%20C_%7B2%7D%20%5Ctimes%2010%20C_%7B4%7D%3D2100)
Thus 2100 different committees that can be formed from 5 teachers and 10 students
Answer:
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Answer:
here is the answer in photo form
Answer:
Difference
Step-by-step explanation:
Remember that the therms of any subtraction problem are minuend, subtrahend, and difference.
- The minuend is the number from which you subtract something. For example, in the subtraction problem 4 -3 = 1, 4 is the minuend (you are subtracting 3 form it).
- The subtrahend is the number you subtract (from the minuend). For example, in 4 - 3 = 1, 3 is the subtrahend (you are subtracting 3 from the minuend 4).
- The difference is the result of subtracting the subtrahend form the minuend, in other words, the result of the subtraction problem. For example, in 4 - 3 = 1, 1 is the difference (the result)
We can conclude that the result of a subtraction problem is called the difference.
Graph the line using the slope and y-intercept, or two points.
(Slope: 4)