Ex-permutations into classes

Ex-permutations into classes - 6 1 1 2 3 2 3 3 = = − B P...

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1 B P F 1 st 2 nd Not done To calculate the number of combinations for n distinguishable items: Three laboratories to be cleaned: Biosorption, Pilot Plant and Fermentation. How many different combinations of cleaning the three laboratories? n=3, r=2 ! )! ( ! r r n n C r n = B P F B P F B P F B P F B P F 3 different combinations 3 ! 2 ! 1 1 * 2 * 3 ! 2 )! 2 3 ( ! 3 = = To calculate the number of permutations for n distinguishable items: Three laboratories to be cleaned: Biosorption, Pilot Plant and Fermentation. How many different sequences of cleaning the three laboratories? n=3, r=2 B P F )! ( ! r n n P r n = 1 st 2 nd Not done 6 different sequences
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Unformatted text preview: 6 ! 1 1 * 2 * 3 )! 2 3 ( ! 3 = = − B P F B P F B P F B P F B P F To calculate the number of permutations with classes: There are three blocks to be ranged and two (No.#2 and No#3) of them are the same. How many orders can the three blacks be arranged? n=3, r=3, n 1 =1, n 2 =2 2 1 3 same 1st arrangement 3 ! 2 ! 1 ! 1 * 2 * 3 ! 2 ! 1 )! 3 3 ( ! 3 ! ! )! ( ! 2 1 = = − = − n n r n n 3 1 2 2 1 3 3 1 2 2 1 3 3 1 2 } } } same, 1st arrangement 2 nd arrangement 3 rd arrangement...
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