11th NCERT Permutations And Combinations

Hi

Question (1)

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that (i) repetition of the digits is allowed? (ii) repetition of the digits is not allowed?Solution

Using the digits 1, 2, 3, 4 and 5 we have to form 3 digit number,(i) Repetation is allowed.

First we will select the digit at hundred place out of 5 given digits. we have 5 options for it.

As the repeatation is allowed we have 5 options for tenth place and for unit place as well.

So the number formed =

= 5 × 5 × 5

= 125.

(ii) repetation is not allowed.

First we will select the digit at hundred place out of 5 given digits. we have 5 options for it.

As the repetation is not allowed, the digit selected at hundredth place will not be repeated.

So we have to select the digit out of 4 options, so we have 4 options.

The digit selected at tenth place will also not be repeated.So for the unit place we have to select the digit out of 3.

The numbers formed

= 5 × 4 × 3

= 60.

Question (2)

How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?Solution

To form the three digit even number using the digits 1, 2, 3, 4, 5, and 6 , the digit at unit place must be even.We have to select one digit out of 2, 4, and 6. It can be done in 3 different ways.

Now repetation of the digits are allowed. So we have 6 possibilites for tenth and hundred place.

So the even number formed with repetation

= 6 × 6 × 3

= 108

Question (3)

How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?Solution

To form 4 letter code we have to use first 10 letters of English and no letter will be repeated.So give 4 positions from 10, it can be done 10P

The number of codes form

= 10P

= 10 × 9 × 8 × 7

= 5040

Question (4)

How many 5–digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?Solution

To form 5–digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67.As the digit can not be repeated , digits 6 and 7 can not be used again in next three digit.

So we have to arrange 3 digits out of remaning 8 digits to form a number , if can be done in 8P

So the number formed

= 8P

= 8 × 7 × 6

= 336

Question (5)

A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?Solution

A coin has to options , either head or tail appears.When 3 coins are tossed for every coin it has 2 options.

So number of possible outcomes

= 2 × 2 × 2

= 8

Question (6)

Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?Solution

There are 5 flag of different colours are given . Using to flag one below the other we have to form single.It can be done in 5P

The number of singles formed

= 5P

= 5 × 4

= 20