The number of words that can be formed using the letters of an "n" letter word taking all at a time ("r" = "n") of which "a" are of one kind, "b" are of another kind, "c" are of a third kind, ...... and "x" are all different such that a + b + c + ... + x = n is given by
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The no. of words that can be formed with the lettes of the word "examinations"
No. of letters in the word "examinations" = 12 {E, X, A, M, I, N, A, T, I, O, N, S}
No. of :
A's = 2 ⇒ No. of letters of the first kind = 2 ⇒ a = 2
I's = 2 ⇒ No. of letters of the second kind = 2 ⇒ b = 2
N's = 2 ⇒ No. of letters of the third kind = 2 ⇒ c = 2
letters which are all different = 6 {E, X, M, T, O, S} ⇒ x = 6
Therefore,
No. of words that can be formed using all the letters of the word "examinations" taking all the letters at a time
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| 12 × 11 × 10 × 9! | | 2 × 1 × 2 × 1 × 2 × 1 |
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165 × 9! |
