A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions.

Question

A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions.

A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is

(a) 196

(b) 280

(c) 346

(d) 140.

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Salim Ahmed Kawsar · Answer 1 · Feb 05, 2023 15:29:48

Correct option: (a) 196

Explanation:

At least 4 from first 5 questions

Total question = 13 and student has to answer 10 questions

∴ He can choose (4 from first 5 and 6 from 8) or (5 from first 5 and 5 from 8)

∴ Number of ways = ⁵C₄ + ⁸C₆ + ⁵C₅ + ⁸C₅

= (5 × 28) + 56

= 196.

Salim Ahmed Kawsar · Answer 2 · Feb 05, 2023 15:29:48

Two cases are possible:

(i) Selecting 4 out of first five questions and 6 out of remaining 8 questions

∴ Number of choices in this case = ⁵C₄ × ⁸C₆ = ⁵C₁ × ⁸C₂ = \(\frac{5\times8\times7}{1\times2}=140\)

(ii) Selecting 5 out of first five questions and 5 out of remaining 8 questions.

⇒ Number of choices =⁵C₅ × ⁸C₅ = 1 × ⁸C₃ = \(\frac{5\times8\times7}{1\times2\times3}=56.\)

∴ Total number of choices = 140 + 56 = 196.

A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions.

2 Answers