Question

A student must answer 7 out of 10 questions on an exam. Find the number n of choices (a) if there are no restrictions, (b) if the student must answer the first two questions, (c) the first or second question but not both. Explain C)

Answer 1

Number of questions on an exam = 10

Number of questions a student must answer = 7

(a) if there are no restrictions

Number of choices = Number of ways of choosing 7 questions from 10 questions =

Number of choices n = 120

(b)

if the student must answer the first two questions

Therefore number of questions left = 10-2=8

Number of questions left to be answered = 7-2=5

Number of choices = Number of ways of choosing 5 questions from 8 questions =

Number of choices = 56

(c) the first or second question but not both

Case 1 :

First question answered :

Number of questions left in the exam = 8 (Since 1st question is answered, student can not answer second question)

Number of questions student left answer = 7-1 =6

Number of ways of choosing 6 questions from 8 questions =

Case 2 :

Second question answered :

Number of questions left in the exam = 8 (Since 2nd question is answered, student can not answer first question)

Number of questions student left answer = 7-1 =6

Number of ways of choosing 6 questions from 8 questions =

Number of choices = Number of choices in case 1 + Number of choices in case 2 = 28+28 = 56

Number of choices = 56