how many four letter arrangements are there for the word Mattawa?
There are 7 letters, so there are 7! ways to arrange them. But, the two t's and 3 a's are indistinguishable.
Since there are 2! ways to arrange the 2 t's, we divide by 2! to get the number of unique permutations.
Similarly for the 3 a's.
So, the final count is 7!/(2!3!) = 120
There are still 7! arrangements, but only 1/6 of them can be distinguished.
I sure am glad you came along and was headed the same way you were but note there are only 4 letters arrangements allowed.
That ended me up with
7!/ [ 4!*3! *3!*2! ]
or
35/12
and a fractional answer did not make sense to me
so Mr. Damon we talked the other day what exactly is your feild my guess is math am i correct
To find the number of four-letter arrangements for the word "Mattawa," we can use the concept of permutations. A permutation is an arrangement of objects where the order matters.
In this case, we need to determine the number of ways we can select and arrange four letters from the word "Mattawa." To do this, we can follow these steps:
Step 1: Find the total number of letters in the word "Mattawa." In this case, there are seven letters.
Step 2: Since we need to select four letters, we need to calculate the number of ways to choose these letters. This can be done using the combination formula. The formula for combinations is:
C(n, r) = n! / (r!(n-r)!)
Where n represents the total number of objects and r represents the number of objects you want to choose.
In our case, we want to choose four letters from a total of seven. Thus, the number of combinations becomes:
C(7, 4) = 7! / (4!(7-4)!)
= 7! / (4!3!)
Step 3: Evaluate the factorials in the above expression. The factorial of a number means multiplying all the whole numbers from 1 to that number.
Therefore,
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040
4! = 4 × 3 × 2 × 1 = 24
3! = 3 × 2 × 1 = 6
Plugging these values back in,
C(7, 4) = 5040 / (24 × 6)
= 35
Therefore, there are 35 four-letter arrangements for the word "Mattawa."