Asked by marth
How many different letter arrangements are possible using all the letters of the word commission?
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Answers
Answered by
GPT 3.5
The word "commission" has 9 letters in total.
To find the number of possible arrangements, we can use the formula for permutations of a set of items:
n! / (n1! * n2! * n3! * ...)
where n is the total number of items and n1, n2, n3, etc. are the number of times each item is repeated.
In the word "commission", we have:
- 1x 'c'
- 2x 'i'
- 2x 'm'
- 2x 's'
- 1x 'o'
- 1x 'n'
Therefore, the total number of arrangements is:
9! / (1! * 2! * 2! * 2! * 1! * 1!)
= 362,880 / (1 * 2 * 2 * 2 * 1 * 1)
= 362,880 / 8
= 45,360
Therefore, there are 45,360 different letter arrangements possible using all the letters of the word "commission".
To find the number of possible arrangements, we can use the formula for permutations of a set of items:
n! / (n1! * n2! * n3! * ...)
where n is the total number of items and n1, n2, n3, etc. are the number of times each item is repeated.
In the word "commission", we have:
- 1x 'c'
- 2x 'i'
- 2x 'm'
- 2x 's'
- 1x 'o'
- 1x 'n'
Therefore, the total number of arrangements is:
9! / (1! * 2! * 2! * 2! * 1! * 1!)
= 362,880 / (1 * 2 * 2 * 2 * 1 * 1)
= 362,880 / 8
= 45,360
Therefore, there are 45,360 different letter arrangements possible using all the letters of the word "commission".
Answered by
GPT 3.5
Apologies for the mistake. Let's try solving it again.
The word "commission" has 10 letters in total. To find the number of different arrangements possible, we can calculate the factorial of the total number of letters, considering that some of the letters are repeated.
So, the number of different arrangements of the word "commission" is:
10! / (2! * 2! * 2!) = 3,628,800 / (2 * 2 * 2) = 3,628,800 / 8 = 453,600
Therefore, there are 453,600 different arrangements possible using all the letters of the word "commission".
The word "commission" has 10 letters in total. To find the number of different arrangements possible, we can calculate the factorial of the total number of letters, considering that some of the letters are repeated.
So, the number of different arrangements of the word "commission" is:
10! / (2! * 2! * 2!) = 3,628,800 / (2 * 2 * 2) = 3,628,800 / 8 = 453,600
Therefore, there are 453,600 different arrangements possible using all the letters of the word "commission".
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