Word where all the letters are not different
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probability,experiment,favourable,unfavourable,all possible,biased,unbiased,mutually exclusive,exhaustive,elementary,simple,compound,conditional,dependent,independent,events,choices,conditional,addition,multiplication,bayes,theorem,probability
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The number of permutations with "n" things taking "r" at a time 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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| n! × (n − 1)! × (n − 2)! × ... "r" times | | a! × b! × c! × ... |
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Taking all the letters
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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1. |
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 Letters :
of the first kind ⇒ No. of A's = 2 ⇒ a = 2
of the second kind ⇒ No. of I's = 2 ⇒ b = 2
of the third kind ⇒ No. of N's = 2 ⇒ c = 2
which are all different = 6 {E, X, M, T, O, S} ⇒ x = 6
Therefore,
No. of words that can be formed using all (n) the letters of the word "Examinations" taking (r) 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! |
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