In an examination, a student to answer 4 questions out of 5 questions;

1.	In an examination, a student to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make a choice.
Answer» Given as The total number of questions = 5 The total number of questions to be answered = 4 The number of ways = we need to answer 2 questions out of the remaining 3 questions as 1 and 2 are compulsory. = ³C₂ On using the formula, ⁿC_r = n!/r!(n – r)! ³C₂ = 3!/2!(3 - 2)! = 3! / (2! 1!) = [3 × 2 × 1] / (2 × 1) = 3 Hence, the no. of ways answering the questions is 3.

In an examination, a student to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make a choice.

Answer»

Given as

The total number of questions = 5

The total number of questions to be answered = 4

The number of ways = we need to answer 2 questions out of the remaining 3 questions as 1 and 2 are compulsory.

= ³C₂

On using the formula,

ⁿC_r = n!/r!(n – r)!

³C₂ = 3!/2!(3 - 2)!

= 3! / (2! 1!)

= [3 × 2 × 1] / (2 × 1)

= 3

Hence, the no. of ways answering the questions is 3.