A student is to answer 10 out of 13 questions in an examination such that he must choose at least four from the first five questions. The number of choices available to him is A.140 B.196 C.280 D.346

Jase Bentley

Jase Bentley

Answered question

2023-01-17

A student is to answer 10 out of 13 questions in an examination such that he must choose at least four from the first five questions. The number of choices available to him is
A.140
B.196
C.280
D.346

Answer & Explanation

mizzxrizzeui

mizzxrizzeui

Beginner2023-01-18Added 5 answers

There are two possible outcomes for the posed question.
(i) Selecting four out of first five questions and six out of remaining eight questions we get 5 C 4 × 8 C 6 = 140 choices.
(ii) Selecting five out of first five questions and five out of remaining eight questions we get 5 C 5 × 8 C 5 = 56 choices.
Hence, the total number of choices is 140 + 56 = 196.

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