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There are 10 questions on a discrete mathematics final exam. How many ways are there to assign scores to the problems if the sum of the scores is 100 and each question is worth at least 5 points?

Respuesta :

Answer:

There are 12,565,671,261 ways.

Step-by-step explanation:

Here we have to use the combination and repetition formula.

C(n + r-1, r) = [tex]\frac{(n + r-1)!}{r!(n-1)!}[/tex]

Given: n = 10 (The number of questions)

Each question is worth at least 5 points.

10 questions = 10 *5 = 50

The total = 100

r = 100 - 50

r = 50

Now we can apply the formula.

C(10 + 50 -1, 50) = [tex]\frac{(10 + 50 -1)!}{50!(10 -1)!}[/tex]

C(59, 50) = [tex]\frac{59!}{50!9!}[/tex]

Simplifying the above factorial using the calculator, we get

C(59, 50) = 12,565,671,261

There are 12,565,671,261 ways.

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