A question paper consist of two part A and B,part A has 6 questions with one alternate each and part B has 8 questions.Find the number of ways by which one can attempt the paper when at leastone question must be attended from each part.
Answers
185640 ways one can attempt the paper when at least one question must be attended from each part
Step-by-step explanation:
A question paper consist of two part A and B,part A has 6 questions with one alternate each and part B has 8 questions
Part A has 6 Question with one alternate each
=> 6 * 2 = 12 Question
if 1 Question answered then it can be done in 12 Ways
if 2 Questions are answered then it can be done in 12 * 10 /2 = 60 ways
(as only 1 can be done from alternate)
if 3 Questions are answered then it can be done in 12 * 10 * 8/ (3 * 2) = 160 ways
if 4 Questions are answered then it can be done in 12 * 10 * 8 * 6/ (4 *3 * 2) = 240 ways
if 5 Questions are answered then it can be done in 12 * 10 * 8 * 6 * 4/ (5 * 4 *3 * 2) = 192 ways
if 6 Questions are answered then it can be done in 12 * 10 * 8 * 6 * 4 * 2/ (6 *5 * 4 *3 * 2) = 64 ways
12 + 60 + 160 + 240 + 192 + 64 = 728 ways
Part B has 8 questions
Total number of ways = ⁸C₁ + ⁸C₂ + ⁸C₃ + ⁸C₄ + ⁸C₅ + ⁸C₆ + ⁸C₇ + ⁸C₈
= 8 + 28 + 56 + 70 + 56 + 28 + 8 + 1
= 255 ways
Total number of ways one can attempt the paper = 728 * 255
= 185640 ways
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