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Zorluk: OrtaCombinations

In a mathematics examination, a student is required to answer 55 questions out of 88 available questions. If the first 22 questions are compulsory, in how many different ways can the student select the questions to answer?

Cevap: 20

Cevap

The student can select the questions in 20 different ways.
With 2 compulsory questions, the student only has to select 3 more questions from the remaining 6 questions. The number of ways to select 3 items from 6 without regard to order is given by ^6C_3 = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20.

Adım Adım Çözüm

1
Deduct compulsory questions from both the required total and available total
The student must choose 3 additional questions from the remaining 6 questions.
Compulsory questions are fixed and provide only 1 selection choice.
2
Apply the combination formula ^6C_3 to calculate selection ways
^6C_3 = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20
The order in which the student chooses the examination questions does not alter the group of questions selected.

Anahtar Kavram

Combinations with restricted/compulsory choices
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Konular

Combinations

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