Hi,

TORONTO , 7 Letters, 2Ts, 3Os

Can be arranged:   ways 

Answer by Theo(13342)   (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.

 

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