Solution1 of Multiplication Rules

The page solution1 of multiplication rules is going to explain some example problems of the concept fundamental rules of counting.

Question 1:

In a class there are 27 boys and 14 girls. The teacher wants to select 1 boy and 1 girl to represent a competition. In how many ways can the teacher make this selection?

Solution:

In a class there are 27 boys and 14 girls. The teacher wants to select 1 boy and 1 girl to represent a competition.

To solve this problem we have to select 1 boy and 1 girl. Here both jobs have to be completed.

Number of ways to make this selection = 27 x 14

                                                     = 378                          

So there are 378 ways to select 1 boy and 1 girl.


Question 2:

Given 7 flags of different colours, how many different signals can be generated if a signal requires the use of two flags, one below the other?

Solution:                    

In this problem we have to select two flags one below the other. To solve this problem we have to use multiplication rule. Because we must select two flags,

Total number of flags = 7

Flag 1    Flag 2

We cannot use selected flag again. We have to use the different flag for flag 2.

For the first place we have 7 options

For the second place we have only 6 options

Number of ways to select two flags = 7 x 6

                                                = 42        

solution1 of multiplication rules  solution1 of multiplication rules


Question 3:

A person wants to buy one fountain pen, one ball pen and one pencil from a stationery shop. If there are 10 fountain pen varieties, 12 ball pen varieties and 5 pencil varieties, in how many ways can he select these articles?

Solution:

Number of fountain pen = 10

Number of ball pen = 12

Number of pencil = 5

Number of ways for selecting 1 fountain pen = 10

Number of ways for selecting 1 ball pen = 12

Number of ways selecting 1 pencil = 5

Number of ways for selecting 1 fountain pen, ball pen,

                                        and pencil = 10 x 12 x 5

                                                       = 600                                                                                                                   Therefore number of ways of selecting 1 fountain pen, 1 ball pen, and 1 pencil = 600