Question

(1 point) How many different 9-letter permutations can be formed from 7 identical H's and two identical T's

Answer 1

To find the number of different 9-letter permutations that can be formed from 7 identical H's and 2 identical T's, we can use the concept of permutations.

Step-by-step explanation:

To find the number of different 9-letter permutations that can be formed from 7 identical H's and 2 identical T's, we can use the concept of permutations.

First, we need to calculate the total number of permutations, which is given by 9! (9 factorial), since there are 9 letters in total.

However, since there are 7 identical H's and 2 identical T's, we need to divide the total number of permutations by the permutations of the identical letters. The number of permutations of the H's is given by 7!, and the number of permutations of the T's is given by 2!.

Therefore, the number of different 9-letter permutations is given by:

9! / (7! * 2!)

Answer 2

There are 36 different 9-letter permutations that can be formed from 7 identical H's and 2 identical T's using the permutations of a multiset formula.

Step-by-step explanation:

Calculating 9-Letter Permutations

To find the number of different 9-letter permutations that can be formed from 7 identical H's and 2 identical T's, we need to use the formula for permutations of a multiset. Here, the total number of letters (n) is 9, and we have 7 H's and 2 T's.

The formula for such permutations is:

n! / (n1! * n2! * ... * nk!)

Where:

• n = Total number of items
  
• n1 = Number of items of type 1
  
• n2 = Number of items of type 2
  
• ...
• nk = Number of items of type k

In our case:

• n = 9 (total letters)
  
• n1 = 7 (number of H's)
  
• n2 = 2 (number of T's)

Using the formula:

9! / (7! * 2!) = 36

Thus, there are 36 different 9-letter permutations that can be formed from 7 identical H's and 2 identical T's.