Find the number of the permutations with the letters of the word TRIANGLE.
there are no duplicates, so this about as simple as it gets.
It has to have been covered on the very first page of your text that introduced the subject. Care to have a go at it?
How many choices for the 1st letter?
the next? the next? ...
40320
To find the number of permutations with the letters of the word "TRIANGLE," we can use the formula for permutations.
The formula for permutations is given by:
P(n, r) = n! / (n - r)!
Where n is the total number of objects and r is the number of objects taken at a time.
In this case, we have the word "TRIANGLE" with 8 letters, so n = 8.
Since we want to find all possible permutations of the letters, we take all 8 letters at a time, so r = 8.
Using the formula:
P(8, 8) = 8! / (8 - 8)!
Simplifying the expression:
8! / 0!
Any number divided by 0! is equal to 1, so:
P(8, 8) = 8! / 0! = 8!
Calculating 8!:
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320
Therefore, the number of permutations with the letters of the word "TRIANGLE" is 40,320.
To find the number of permutations with the letters of the word "TRIANGLE," we need to determine how many ways we can arrange these letters.
Step 1: Count the total number of letters in the word. In this case, there are 3 R's, 1 T, 1 I, 1 A, 1 N, 1 G, and 1 L. So, we have a total of 3 + 1 + 1 + 1 + 1 + 1 + 1 = 9 letters.
Step 2: Find the factorial of the total number of letters. The factorial of a number is the product of that number and all the positive integers below it. In this case, the factorial of 9 is denoted as 9! and calculated as follows:
9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880
So, there are 362,880 ways to arrange the letters of the word "TRIANGLE."