Unit:- Count the ways - IShalabh and his family of three – Anjali, son Mohit and daughter Kuhu are excited to take the first ride in the new car!There are five seats in the car, two in front and three at the back.Shalabh is sitting at the driver’s seat, waiting for the family. Kuhu, the youngest child of the family hops into the car and takes a seat at the back of the car.How many seats are vacant now? Yes, three!How many more people are yet to take a seat in the car? Two!This means that Anjali and Mohit get to sit in any of the three vacant seats.In how many ways can they be seated int the three vacant seats? Let us find out…Fundamental Counting Principle of Multiplication says; if one event can occur in number of ways followed by a second event, that can occur in number of ways. Then, the two events taken together can be performed in ways. This concept can be extended to any finite number of events to occur together.Let Anjali take one of the vacant seats in the car. Total number on ways for Anjali to take a seat = 3 ways In how many ways can Mohit take a seat in the car now that Anjali is seated?There are two vacant seats available for Mohit to choose from. Total number on ways for Mohit to take a seat = 2 waysTherefore, according to the Fundamental Principle of Counting, the total number of ways Anjali and Mohit to sit in the car = 3 × 2 = 6 ways Question 1: Mohit is taking a MCQ class test consisting of five questions. Each question has two choices – True or False. What is the total number of ways Mohit can answer all five questions (irrespective of Correct or Incorrect answer)? *
2 points
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a) 6 ways
b) 32 ways
c) 16 ways
d) 8 ways
Answers
Given : Mohit is taking a MCQ class test consisting of five questions.
Each question has two choices – True or False.
To Find : What is the total number of ways Mohit can answer all five questions (irrespective of Correct or Incorrect answer)?
a) 6 ways
b) 32 ways
c) 16 ways
d) 8 ways
Solution:
Each question has two choices – True or False.
Hence Each Question can be answered in 2 ways
There are total 5 Questions - All has to be answered
Hence total ways to answer = 2 * 2 * 2 * 2 * 2
= 2⁵
= 32
There are 32 ways Mohit can answer all five questions
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Answer:
Correct answer is option B