Question

(i) Count the total number of ways of answering 6 objective type questions, each question having 4 choices.

(ii) In how many ways 10 pigeons can be placed in 3 different pigeon holes ?

(iii) Find the number of ways of distributing 12 distinct prizes to 10 students?

Answer 1

(i) Count the total number of ways of answering 6 objective type questions, each question having 4 choices. 

One question can be answered in 4 ways 

Two questions can be answered in 4 × 4 = 4² ways 

∴ Six questions can be answered in 46 ways

(ii) First pigeons can be placed in pigeon hole in 3 ways (selecting 1 from 3 holes) 

Second pigeons can be placed in pigeon hole in 3 ways Tenth pigeons can be placed in pigeon hole in 3 ways 

So total number of ways in which all the number 10 place can be sent = 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 = 310 ways

(iii) To give the first prize we have to select, from the 10 students which can be done in 10 ways. 

To give the second prize we have to select one from the 10 students which can be done is 10 ways. 

To give the 12th prize we have to select one from 10 students which can be done in 10 ways. 

So all the 12 prizes can be given in (10 × 10 × 10 … 12 times) = 1012 ways.