There are 6 multiple choice questions in an examination. How many sequ

1.	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 2 each?
Answer» 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

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 2 each?

Answer»

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