How many different strings can be made from the letters in STATISTICS, using all the letters
There are 10 letters, with 3 S's, 3 T's, 2 I's, so
10!/(3!3!2!) = 50400
To calculate the number of different strings that can be made from the letters in the word "STATISTICS" using all the letters, we can use the concept of permutations.
First, let's count the number of occurrences of each letter in the word:
- The letter "S" appears 3 times.
- The letter "T" appears 3 times.
- The letter "A" appears 1 time.
- The letter "I" appears 2 times.
- The letter "C" appears 1 time.
To find the number of different strings, we need to calculate the number of permutations. The formula for permutations with repetition is:
n! / (n1! * n2! * ... * nk!)
Where n is the total number of items and n1, n2, ..., nk are the number of occurrences of each item.
Using this formula, let's calculate the number of different strings:
n = 10 (total number of letters in "STATISTICS")
n1 = 3 (number of occurrences of "S")
n2 = 3 (number of occurrences of "T")
n3 = 1 (number of occurrences of "A")
n4 = 2 (number of occurrences of "I")
n5 = 1 (number of occurrences of "C")
applying the formula:
10! / (3! * 3! * 1! * 2! * 1!)
Calculating this expression:
10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3,628,800
3! = 3 * 2 * 1 = 6 (for "S")
3! = 3 * 2 * 1 = 6 (for "T")
1! = 1 (for "A")
2! = 2 * 1 = 2 (for "I")
1! = 1 (for "C")
So, the final calculation is:
3,628,800 / (6 * 6 * 1 * 2 * 1) = 3,628,800 / 144 = 25,200
Therefore, there are 25,200 different strings that can be made from the letters in "STATISTICS" using all the letters.
To find the number of different strings that can be made from the letters in STATISTICS, using all the letters, you can use the concept of permutations.
Here's how you can calculate it step by step:
1. Start by counting the number of times each letter appears in the word "STATISTICS":
- There are 3 'S's
- There are 3 'T's
- There are 2 'I's
- There are 1 'A' and 1 'C'
2. Calculate the total number of permutations using the formula for permutations with repeated elements:
- P = (total number of letters)! / (number of repetitions of first letter! * number of repetitions of second letter! * ... * number of repetitions of last letter!)
In this case, the formula becomes:
- P = 10! / (3! * 3! * 2! * 1! * 1!) = 10! / (3!^2 * 2!) = 10! / 36
3. Simplify the expression:
- 10! means multiplying all the positive integers from 1 to 10: 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
- 3!^2 means multiplying 3! by itself: 3! * 3! = 3 * 2 * 1 * 3 * 2 * 1 = 36
4. Perform the calculation:
- P = 10! / 36
Using a calculator or computer program, you can find the value of P to be approximately 14,400.
Therefore, there are approximately 14,400 different strings that can be made from the letters in STATISTICS, using all the letters.