In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.

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Solution

A student has to answer 4 question out of 5 questions.
Since questions 1 and 2 are compulsory, he/she will have to answer 2 question from the remaining 3.
∴ Required number of ways = $^{3} C_{2} = 3$

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In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.

A student has to answer 4 question out of 5 questions. Since questions 1 and 2 are compulsory, he/she will have to answer 2 question from the remaining 3. ∴ Required number of ways =3C2 = 3

A student has to answer 4 question out of 5 questions.
Since questions 1 and 2 are compulsory, he/she will have to answer 2 question from the remaining 3.
∴ Required number of ways = $^{3} C_{2} = 3$