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shtirl [24]
3 years ago
14

A committee consisting of 4 faculty members and 5 students is to be formed. Every committee position has the same duties and vot

ing rights. There are 8 faculty members and 13 students eligible to serve on the committee. In how many ways can the committee be formed?
Mathematics
1 answer:
MArishka [77]3 years ago
8 0

Answer:

Step-by-step explanation:

This question bothers on combination. combination has to do with selection.

If 4 faculty members are chosen from total of  8 faculty members, this can be done in 8C4 number of ways.

8C4 = 8!/(8-4)!4!

8C4 = 8!/4!4!

8C4 = 8*7*6*5*4!/4!*4*3*2

8c4 = 8*7*6*5/24

8C4 = 7*5*2

8C4  =70 ways

Similarly,  5 students are to be selected from a pool of 13 students, this can be done in 13C5 number of ways.

13C5 = 13!/(13-5)!5!

13C5 = 13!/8!5!

13C5 = 13*12*11*10*9*8!/8!*5*4*3*2

13C5 = 13*12*11*10*9/120

13C5 = 1,287 ways

The total number of ways the committee can be formed is 8C4 * 13C5 = 70*1287

The total number of ways the committee can be formed is 90,090 ways

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The area of a rectangular wall of a barn is 85 square feet. Its length is 12 feet longer than the width. Find the length and wid
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Answer:

Length = 17 feet, Width = 5 feet

Step-by-step explanation:

Given:

The area of a rectangular wall of a barn is 85 square feet.

Its length is 12 feet longer than the width.

Question asked:

Find the length and width of the wall of the barn.

Solution:

Let width of a rectangular wall of a barn = x

<u>As length is 12 feet longer than the width.</u>

Length of a rectangular wall of a barn = 12+x

As we know:

Area\ of\ rectangle=length\times breadth

85=(12+x)x\\\\85=12x+x^{2} \\

Subtracting both sides by 85

x^{2} +12x-85=0\\x^{2} +17x-5x-85=0\\Taking\ common\\x+(x+17)-5x(x+17)=0\\(x+17)(x-5)=0\\x+17=0, x-5=0\\x=-17,x=5

As width can never be in negative, hence  width of a rectangular wall of a barn = x = 5 feet

Length of a rectangular wall of a barn = 12+x=12+5=17\ feet

Therefore, length and width of the wall of the barn is 17 feet and 5 feet respectively.

                 

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