Permutations and CombinationsDate: 10/22/96 at 23:51:21 From: Monique Jain Subject: Permutations and Combinations How many different six-digit numbers can be formed using three 5's, two 4's, and one 6? I used 6x5x4x3x2x1 = 720 - is that correct? Date: 10/23/96 at 5:32:46 From: Doctor Anthony Subject: Re: Permutations and Combinations No. You have 6 numbers altogether to use, and if these were all different then the number of different six-digit numbers would be 6! = 720. However, this number is too large because the 5's could be swapped amongst themselves without giving rise to a different six-digit number, and similarly the 4's could be swapped without producing a different six-digit number. The three 5's could be rearranged in 3! = 6 ways, and the two 4's in 2! = 2 ways. So altogether the number 720 is too large by a factor 6 x 2 = 12. The correct answer is 720/12 = 60. -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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