what is the number of distinguishable permutations of the word hippopotamus?
You asked this earlier, and I showed you how to do Mississippi. Use the same approach for hippo...
How about 12!/(3!*2!)= ?
I assume you know the meaning of ! (factorial)
To find the number of distinguishable permutations of the word "hippopotamus," we can use the concept of combinations and permutations.
Step 1: First, we need to determine the total number of letters in the word "hippopotamus." In this case, there are 12 letters.
Step 2: Next, we need to account for repeating letters. In the word "hippopotamus," there are 3 'P's and 2 'O's. We divide the total number of letters by the number of repeating letters:
12! / (3! * 2!)
Explanation: The formula 12! / (3! * 2!) is used to calculate the number of distinguishable permutations. The exclamation symbol (!) represents the factorial of a number, which is the product of all positive integers less than or equal to that number.
The denominator contains the factorials of the repeating letters ('P' and 'O') to account for the overcounting that would arise if all the letters were distinct.
Step 3: Perform the calculation:
12! / (3! * 2!) = (12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / ((3 * 2 * 1) * (2 * 1))
= 479,001,600 / (6 * 2)
= 479,001,600 / 12
= 39,900,133,333,333,333,333,333,333,333,333
Therefore, the number of distinguishable permutations of the word "hippopotamus" is 39,900,133,333,333,333,333,333,333,333,333,333.
To find the number of distinguishable permutations of the word "hippopotamus," we need to calculate the factorial of the total number of letters in the word.
The word "hippopotamus" has 12 letters in total.
The factorial of a number is the product of all positive integers less than or equal to that number. For example, the factorial of 3 (written as 3!) is 3 × 2 × 1 = 6.
In this case, we need to calculate the factorial of 12 (12!).
Calculating the factorial can be done manually by multiplying each number starting from 12 and going down to 1:
12! = 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
Or, you can use a calculator, a spreadsheet program, or a mathematical software to calculate the factorial automatically.
The calculated value should give you the number of distinguishable permutations of the word "hippopotamus."