# SOLUTION: What is the number of arrangements that can be made out of the letters of the words "SUCCESS" so that all the S do not come together?

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 Click here to see ALL problems on Permutations Question 4565: What is the number of arrangements that can be made out of the letters of the words "SUCCESS" so that all the S do not come together?Answer by khwang(438)   (Show Source): You can put this solution on YOUR website! Among "SUCCESS", there are 3 S, 2 C , 1 U & 1 E. So, there are 7!/(3! 2!) = (7*6*5*4)/2 = 420 possible arrangements When all 3 S come together , there are (1+2+1+1)!/2! = 5!/2! = 60 Hence, there are 420-60 = 360 arrangements that all the S do not come together. Kenny