Question

Find the number of 4-letter words with or without meaning which can be formed out of the letters of the word KENY when, (i) The repetition of letters is not allowed. (ii) E is at first place​

Answer 1

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...

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