Question

How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter Exactly once?​

Answer 1

Answer:

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Solution:

☣️Number of letters in word EQUATION` = 8

n = 8

☣If all letters of the word used at a time

r = 8

Different numbers formed = nPr

= 8P8

= 8!/(8 8)!

= 8!/0!

= 8!/1

= 8!

= 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

= 40320

$\boxed{\sf\red{= 40320}}$

Answer 2

Answer:

There are 8 different letters in the word EQUATION. 

The first place can be filled in 8 ways.

Second place can be filled by any one of the remaining 7 letters. So, second place can be filled in 7 ways

Third place can be filled by any one of the remaining 6 letters. So, third place can be filled in 6 ways

So, on continuing, number of ways of filling fourth place in 5 ways , fifth place in 4 ways, six place in 3 ways, seventh place in 2 ways, eighth place in 1 way.

Therefore, the number of words that can be formed using all the letters of the word EQUATION, using each letter exactly once is 8×7×6×5×4×3×2×1=8!

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