Question

A question paper is divided in three groups A,B and C each of which contains 3 question, each of 25 marks. One examinee is required to answer 4 question taking at least one from each group. in how many ways he can cboose the question to answer 100 marks.​

Answer 1

( 2,1,1) in

$\binom{3}{2} \times \binom{3}{1} \times \binom{3}{1} \: ways$

$= 27 \: ways$

(1,2,1) in

$\binom{3}{1} \times \binom{3}{2} \times \binom{3}{1} \: ways$

$= 27 \: ways$

(1,1,2) in

$\binom{3}{1} \times \binom{3}{1} \times \binom{3}{2} ways$

$27 \: ways$

$there \: are \: 27 + 27 + 27 = 81 \: ways$