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zhenek [66]
3 years ago
13

A college committee consists of 3 freshmen, 4 sophomores, 5 juniors, and 2 seniors. A subcommittee of 4 consisting of 1 person f

rom each class is to be chosen. How many different subcommittees are possible?
Mathematics
1 answer:
dezoksy [38]3 years ago
5 0

Answer:

120

Step-by-step explanation:

The subcommittee needs to contain 1 out of 3 freshmen, 1 out of 4 sophomores, 1 out of 5 juniors and 1 out of 2 seniors. Assuming order is not important, the number of possibilities to pick the subcommittee members is given by:

N=5*4*3*2=120

There are 120 possible subcommittees.

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Solution:

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Solve using mid-point formula:

$\text{Midpoint} =\left( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right  )

Here x_1=m, y_1=n, x_2=h, y_2=0

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$\text{Midpoint} =\left( \frac{m+h}{2}, \frac{n}{2}\right  )

<u>To find the missing coordinate:</u>

Let the missing coordinates by x and y.

Here x_1=0, y_1=0, x_2=x,  y_2=y

$\text{Midpoint}=\left( \frac{0+x}{2}, \frac{0+y}{2}\right  )

$\left( \frac{m+h}{2}, \frac{n}{2}\right  )=\left( \frac{0+x}{2}, \frac{0+y}{2}\right  )

$\left( \frac{m+h}{2}, \frac{n}{2}\right  )=\left( \frac{x}{2}, \frac{y}{2}\right  )

Now equate the x-coordinate.

$ \frac{m+h}{2}=\frac{x}{2}

Multiply by 2 on both sides of the equation, we get

m + h = x

x = m + h

Now equate the y-coordinate.

$\frac{n}{2} =  \frac{y}{2}

Multiply by 2 on both sides of the equation, we get

n = y

y = n

Hence the missing coordinates of the parallelogram is (m + h, n).

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