There are 6 multiple choice questions in an examination. How many sequences of answers are possible,

Question

There are 6 multiple choice questions in an examination. How many sequences of answers are possible,

There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 5 choices each?

Share with your friends

Talk Doctor Online in Bissoy App

Salim Ahmed Kawsar · Answer 1 · Feb 05, 2023 15:29:48

Each of the first three questions can be answered in 4 ways and each of the next three questions can be answered in 5 different ways.
Hence, the required number of different sequences of answers = 4 × 4 × 4 × 5 × 5 × 5 = 8000.

Salim Ahmed Kawsar · Answer 2 · Feb 05, 2023 15:29:48

Given as

Multiple choice question, only one answer is correct of the given options.

For the first three questions only one answer is correct out of four. Therefore it can be answered in 4 ways.

The total number of ways to answer the first 3 questions = ⁴C₁ × ⁴C₁ × ⁴C₁ = 4 × 4 × 4 = 64

Each of the next 3 questions can be answered in 2 ways.

The total number of ways to answer the next 3 questions = ²C₁ × ²C₁ × ²C₁ = 2 × 2 × 2 = 8

Thus, total possible outcomes possible are 64 × 8= 512

Salim Ahmed Kawsar · Answer 3 · Feb 05, 2023 15:29:48

Given :

Multiple choice question, only one answer is correct of the given options.

So, for the first three questions only one answer is correct out of four, similarly, for the remaining three question, only one answer is correct out of two.

Number of outcomes possible is ⁴C₁ × ⁴C₁ × ⁴C₁ for the first three and ²C₁ × ²C₁ × ²C₁ for the remaining three.

Hence,

Total possible outcomes possible are ⁴C₁ × ⁴C₁ × ⁴C₁ × ²C₁ × ²C₁ × ²C₁ = 512

There are 6 multiple choice questions in an examination. How many sequences of answers are possible,

3 Answers