# I need to solve the following two problems. I am not sure how to solve them and I'm not sure if the process is different for the first one and the second one, mostly because a letter is repeated...

I need to solve the following two problems.

I am not sure how to solve them and I'm not sure if the process is different for the first one and the second one, mostly because a letter is repeated in the second one.

How many permutations are there of the letters in the word “HEART”?

How many permutations are there of the letters in the word “AMAZING”?

Asked on by catd1115

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The number of permutations of the letters of the word HEART can be found in the following way. You can place any of the 5 letters in the first place of the word. For the second place we have the remaining 4 letters, this goes on till there is only 1 letter for the 5th place.

The number of permutations is the product of 5, 4, 3, 2 and 1 or 5*4*3*2*1 = 120

For the word AMAZING, A is repeated twice. The number of permutations here can be found as above except here take care of the letter that is repeating by dividing the factorial of the total number of letters by the factorial of the number of times the letter A repeats. This gives the result as 7!/2! = 2520

The number of permutations of the letters of the word HEART is 120 and that of the letters of the word AMAZING is 2520

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