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!
Answers & Comments
Answer:
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
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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