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A Candidate is Required to Answer 7 Questions Out of 12 Questions Which Are Divided into Two Groups, Each Containing 6 Questions. He is Not Permitted to Attempt More than 5 Questions from Either - Mathematics

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प्रश्न

A candidate is required to answer 7 questions out of 12 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. In how many ways can he choose the 7 questions?

उत्तर

Required ways = 

\[{}^6 C_5 \times^6 C_2 +^6 C_4 \times^6 C_3 + {}^6 C_3 \times^6 C_4 + {}^6 C_2 \times^6 C_5\]
\[= 2\left( {}^6 C_5 \times^6 C_2 +^6 C_4 \times^6 C_3 \right)\]
\[ = 2\left( 90 + 300 \right)\]
\[ = 2\left( 390 \right)\]
\[ = 780\]
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अध्याय 17: Combinations - Exercise 17.2 [पृष्ठ १६]

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आरडी शर्मा Mathematics [English] Class 11
अध्याय 17 Combinations
Exercise 17.2 | Q 13 | पृष्ठ १६

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