An examination paper consists of 12 questions diyided in to part A and B. Part A contains 7 questions and part B contains 5 questions. A candidate is required to attempt 8 questions, selecting atleat 3 questions from each part. In how many ways can the candidate select the questions ?

Explanation

Candidate has to select atleast 3Q from each part.
`therefore` Different possibilities are
5 from A and 3 from B
or 4 from A and 4 from B
or 3 from A and 5 from B
`therefore` Number of selections `= .^(7)C_(5).^(5)C_(3)+.^(7)C_(4).^(5)C_(4)+.^(7)C_(3).^(5)C_(5)`
`= 21.10+35.5+35.1`
`=210+175+35=420`