# SOLUTION: In how many distinct ways can the TORONTO be arranged

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 Question 632059: In how many distinct ways can the TORONTO be arrangedFound 2 solutions by ewatrrr, Theo:Answer by ewatrrr(10682)   (Show Source): You can put this solution on YOUR website! ``` Hi, TORONTO , 7 Letters, 2Ts, 3Os Can be arranged: ways ```Answer by Theo(3464)   (Show Source): You can put this solution on YOUR website!7!/(3!*2!) = 7*6*5*4*3*2*1 / 3*2*1*2*1 which is equal to 420 7! if all the letters were different. Since 3 O's are common, you have to divide by 3!. Since 2 T's are common, you have to divide by 2!. Hard to see with 7 letters. Easier to see with 3. Assume letters are a,b,c possible permutations are: a,b,c a,c,b b,a,c b,c,a c,a,b c,b,a that's a total of 6 which is equal to 3! Now assume 2 of the letters are the same. let's assume it's b. then the letters are a,b,b possible permutations are: a,b,b b,a,b b,b,a that's a total of 3 which is equal to 6! / 2! = 3 same concept applies to 7 letters but the number of permutations is too large to list separately. TORONTO has 2 of the letter T and 3 of the letter O and 1 each of the rest. formula becomes 7! / (3!*2!) which is equal to 7*6*5*4*3*2*1 / 3*2*1*2*1 which is equal to 7*6*5*2 which is equal to 420.