A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?
A. 63
B. 511
C. 1023
D. 15
Answers
Answer:
1023
Step-by-step explanation:
A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?
He can attempt Each Question Using any of three Given options or can choose not to answer That
=> 4 Options for Each Question
Total are 5 Question.
=> 4 * 4 * 4 * 4 * 4
= 1024
But this consist of one case Where he opted not to answer for Every Question
=> ways can a candidate attempt one or more problems = 1024 - 1 = 1023
Other Way to solve
He may attempt 5 , 4 , 3 , 2 or 1 Question
Attempted 5 = ⁵C₅ * 3⁵ = 243
Attempted 4 = ⁵C₄ * 3⁴ = 405
Attempted 3 = ⁵C₃ * 3³ = 270
Attempted 2 = ⁵C₂ * 3² = 90
Attempted 1 = ⁵C₁ * 3¹ = 15
Adding all = 243 + 405 + 270 + 90 + 15 = 1023