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soldi70 [24.7K]
2 years ago
10

An exam has 10 problems. How many ways can (integer points be assigned to the problems if the total of the points is 100 and eac

h problem is worth at least 5 points?
Mathematics
1 answer:
vovikov84 [41]2 years ago
7 0

Answer:

number of way is \frac{59!}{50)!9!}

Step-by-step explanation:

given data:

total number of problems 100

total points for each problem 5

let ten problems are

x_1, x_2,........., x_{10}

according to the given information

x_1 +x_2 +.......+x_{10} = 100

x_i \geq 5

where i =1 + 10

so, number of way integer point can assign are

   ^{(n+r-1)}C_{(r-1)}

where

r = 10

n = 100 - 10\times 5 = 50

so, we have

^{(59)}C_{9}

\frac{59!}{59-9)!9!}

number of way is \frac{59!}{50)!9!}

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Step-by-step explanation:

If you attempt to solve this by clearing fractions, you end up with an extraneous solution. Here, we'll solve the linear equations ...

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_____

<em>Additional comment</em>

If you graph these equations, you find they describe hyperbolas that intersect at (0, 0) and (4, 4). The "solution" (0, 0) is extraneous, as both equations are undefined there.

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