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How many 5-digit permutations can be formed from the set S={1,2,3,4,5,6,7,8,9} provided the three digits {1, 5, 8} are together in every permutations in any of 3! ways? Thank you.

 May 3, 2023
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If we group the 3 digits (1, 5, 8) as one digit, then we have 6 + 1 = 7 digits

 

1 - If the permutation begins with (1, 5, 8), the we have: 3! x 6 x 5 = 180 permutations

 

2 - If the permutation begins with one the other 6 digits, then we have: 6 x 3! x 5 =180 permutations

 

3 - If the permutation begins with 2 of the other 6 digits, then we have: 6 x 5 x 3! =180 permutations =

 

4 - So, the grand total =180 x 3 =540 permutations.

 May 4, 2023

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