IF THERE ARE 10 QUESTIONS IN A QUESTION PAPER WITH YES, NO ANSWERS THEN NUMBER OF WAYS HE CAN ANSWER THE QUESTION PAPER WHEN I)NEED TO ATTEMPT ALL QUESTIONS 2)NEED TO ATTEMPT AT LEAST ONE QUESTION 3)ALLOWED FOR NOT ATTEMPTING ANY QUESTION OR SOME QUESTIONS.

Asked by gayathri | 13th Sep, 2012, 09:46: PM

Expert Answer:

 There are 10 questions in the question paper, each question can be answered in 2 ways (Either YES or NO).

 

(1)    Therefore, the number of ways that he answers all questions = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 210 = 1024.

 

(2)    To attempt at least one question, he may attempt either of 1, 2, 3, 4, 5, 6, 7, 8, 9 and      10 questions.

 

Out of 10 questions, 1 question can be selected in 10C1 ways.

Each of these questions can be answered in 21 ways.

So, 1 question can be answered in 10C1 × 21 ways.

 

Out of 10 questions, 2 questions can be selected in 10C2 ways.

Any of these 2 questions can be answered in 22 ways.

So, 2 questions can be answered in 10C2 × 22 ways.

 

Similarly, the number of ways in which he answers at least one question

= 10C1 × 21 + 10C2 × 22 + 10C3 × 23 + 10C4 × 24 + 10C5 × 25 + 10C6 × 26 + 10C7 × 27 + 10C8 × 28 + 10C9 × 29 + 10C10 × 210

= (10C0 × 20 + 10C1 × 21 + 10C2 × 22 + 10C3 × 23 + 10C4 × 24 + 10C5 × 25 + 10C6 × 26 + 10C7 × 27 + 10C8 × 28 + 10C9 × 29 + 10C10 × 210) - 10C0 × 20

= (2 + 1)10 - 1

= 310 - 1

 

(3)    No question can be answered in only 1 way.

Some questions i.e. at least one question can be answered in (310 - 1) ways.

 

So, no question or some questions can be answered in (310 - 1) + 1 = 310 ways.

 

Answered by  | 14th Sep, 2012, 10:35: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.