Ex 7.3, 10 - In how many distinct permutations in MISSISSIPPI - Ex 7.3

  1. Class 11
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Ex7.3, 10 In how many of the distinct permutations of the letters in MISSISSIPPI do the four I s not come together? Total number of permutation of 4I not coming together = Total permutation total permutation of I coming together In MISSISSIPPI there are 4I, 4S, 2P and 1M Since letter are repeating we will use the formula = !/ 1! 2! 3! Total number of alphabet = 11 Hence n = 11, there are 4I, 4S, 2P p1 = 4, p2 = 4, p3 = 2 Hence total number of permutation = !/ 1! 2! 3! = 11!/4!4!2! = (11 10 9 8 7 6 5 4!)/((4 3 2 1) (2 1)(4!)) = 34650 Now taking 4Is as one, MISSISSIPPI Here, there are repeating letters So, we use the formula , Number of permutation = !/ 1! 2! Number of letters = 8 Since there are 4 S & 2p p1 = 4, p2 = 2, Number of permutation with 4I together = !/ 1! 2! = 8!/4!2! = 840 Total number of permutation of 4I not coming together = Total permutation total permutation of I coming together = 34650 840 = 33810

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