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Standard XII

Mathematics

Combination

In a examinat...

Question

In a examination, a student has to answer $8$ questions out of $10$ questions. If questions $1$ and $10$ are compulsory, in how many ways can a student choose the questions?

20

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24

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28

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30

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Solution

The correct option is C $28$
Q's 1 and 10 are compulsory.
The remaining 6 questions can be chosen in $^{8} C_{6}$ ways = $\frac{8!}{2! 6!} = \frac{4 \times 7}{2} = 28$

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In a examination, a student has to answer 8 questions out of 10 questions. If questions 1 and 10 are compulsory, in how many ways can a student choose the questions?

The correct option is C 28Q's 1 and 10 are compulsory.The remaining 6 questions can be chosen in 8C6 ways = 8!2!6!=4×72=28

In a examination, a student has to answer $8$ questions out of $10$ questions. If questions $1$ and $10$ are compulsory, in how many ways can a student choose the questions?

The correct option is C $28$
Q's 1 and 10 are compulsory.
The remaining 6 questions can be chosen in $^{8} C_{6}$ ways = $\frac{8!}{2! 6!} = \frac{4 \times 7}{2} = 28$