Question

Question:-

Find the number of 4 letter words , with or without meaning , which can be formed out of the letters of the word ROSE , where the repetition of the letters

(1) is not allowed
(2) is allowed

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Answer 1

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$\huge\bold{Solution}$

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Here, total number of words will be equal to the number of ways of filling 4 vacant places by the 4 letters of the word ROSE.

(1). When the repetition of the letters is not allowed

Here , vacant places are 4 I.e. |__|__|__|__|

First place can be filled by anyone of the 4 letters .

.•. Number of ways of filling first place = 4

Now , Second place can be filled by anyone of the remaining 3 letters.

No. of ways of filling 2nd place = 3

Similarly, third place can be filled by anyone of the remaining 2 letters and fourth place is filled by last letter.

.•.

Since , Each place can be filled after filling the previous place..

So, by FPM (Fundamental Principle of Multiplication) , required no. of ways

= 4 × 3 × 2 × 1

= 24 ways.

(2).

When the repetition is allowed,

Here , out of 4 vacant places , each place can be filled by 4 letters .

.•. Required no. of ways

= 4 × 4 × 4 × 4

= 256 ways..

Hence , number of 4 letters word is 24 when repetition is not allowed and 256 ways when repetition is allowed...

Hope it helps you out✔✔✔

Answer 2

Answer:

(1) 24

(2) 256

Step-by-step explanation:

Our given word is ROSE .

CASE 1 :

Repetition is not allowed .

Firstly there are 4 possibilities for the first letter .

Then the number of possibilities become 3 because one digit is reduced.

Then the possibility is 2 .

Then only 1 letter can be placed.

By Principle of counting :

Number of words = 1 × 2 × 3 × 4

                              = 24

24 words can be formed if repetition is not allowed .

CASE 2 :

If repetition is allowed ,

Then all spaces have 4 chances .

Number of words = 4 × 4 × 4 × 4

                             = 256

So 256 words can be found with repletion.