Question -
Answer -
Given:
Total number ofquestions = 12
Total number ofquestions to be answered = 7
Number of ways = (No.of ways of answering 5 questions from group 1 and 2 from group 2) + (No. ofways of answering 4 questions from group 1 and 3 from group 2) + (No. of waysof answering 3 questions from group 1 and 4 from group 2) + (No. of ways ofanswering 2 questions from group 1 and 5 from group 2)
= (6C5┬а├Ч┬а6C2)+ (6C4┬а├Ч┬а6C3) + (6C3┬а├Ч┬а6C4)+ (6C2┬а├Ч┬а6C5)
By using the formula,
nCr┬а= n!/r!(n тАУ r)!
= (6├Ч15) + (15├Ч20) +(20├Ч15) + (15├Ч6)
= 90 + 300 + 300 + 90
= 780
тИ┤┬аThe total no. ofways of answering 7 questions is 780 ways.