Permutation

Exercise 16.2

QUESTION 1

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

Sol :

No. of boys in the class = 27

No. of Girls in the Class = 14

Ways to select a boy = 27

Similarly, ways to select a girl = 14

\therefore Number of ways to select 1 boy and 1 girl = 27 \times 14 = 378

 

QUESTION 2

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?

Sol :

Number of fountain pen varieties =10

Number of ball pen varieties =12

Number of pencil varieties = 5

Ways to select a fountain pen =10 

Ways to select a ball pen = 12

Ways to select a pencil = 5

(by using the fundamental principle of multiplication)

Ways to select a fountain pen, a ball pen and a pencil =10 \times 12\times 5 = 600

 

QUESTION 3

From Goa to Bombay there are two roots; air and sea. From Bombay to Delhi there are three routes; air, rail and road. From Goa to Delhi via Bombay, how many kinds of routes are there?

Sol :

Number of routes from Goa to Bombay = 2

Number of routes from Bombay to Delhi = 3

(by using the fundamental principle of multiplication)

 

QUESTION 4

A mint prepares metallic calendars specifying months, dates and days in the form of monthly sheets (one plate for each month). How many types of calendars should it prepare to serve for all the possibilities in future years?

Sol :

The f‌irst day of the year can be any one of the days of the week, i.e the f‌irst day can be
selected in 7 ways.

But, the year could also be a leap year.

So, the mint should prepare 7 calendars for the non-leap year and 7 calendars for the
leap year.

So, total number of calendars that should be made = 7 + 7 = 14

 

QUESTION 5

There are four parcels and five post-offices. In how many different ways can the parcels be sent by registered post?

Sol :

Number of ways of sending 1 parcel via registered post = 5

Number of ways of sending 4 parcels via registered post through 5 post off‌ices = 5 \times  5 \times 5 \times 5 = 625

 

QUESTION 6

A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?

Sol :

Number of outcomes when the coin is tossed for the f‌irst time = 2

Number of outcomes when the coin is tossed for the second time = 2

Thus, there would be 2 outcomes, each time the coin is tossed.

Total number of possible outcomes on tossing the coin f‌ive times = 2\times 2\times 2\times 2\times 2 = 32

 

QUESTION 7

In how many ways can an examine answer a set of ten true/false type questions?

Sol :

Number of ways of answering the f‌irst question = 2 (either true or false)

Similarly, each question can be answered in 2 ways.

\thereforeTotal number of ways of answering all the 10 questions = 2 \times 2 \times 2 \times 2\times 2\times 2\times 2\times 2\times 2 \times 2 =1024

 

QUESTION 8

A letter lock consists of three rings each marked with 10 different letters. In how many ways it is possible to make an unsuccessful attempt to open the lock?

Sol :

 

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