how many distinct letter words can be made from the word "CHRISTYNA"?
since the letters of the word "CHRISTYNA" are all distinct selecting distinct letters from "CHRISTYNA" can be done as follows:we partition the distinct letters according to the sizes of words want.9c1+9c2.2!+9c3.3!+9c4.4!+9c5.5!+9c6.6!+9c7.7!+9c8.8!+9c9.9!.
To find the number of distinct letter words that can be made from the word "CHRISTYNA," you need to consider that some letters are repeated.
Here is how you can solve this problem step by step:
1. Begin by counting the total number of letters in the word "CHRISTYNA." In this case, there are 9 letters.
2. Identify any repeated letters in the word. In "CHRISTYNA," the letters 'I' and 'T' appear twice each.
3. Calculate the factorial of the total number of letters. The factorial is denoted by '!,' and it represents the product of all positive integers less than or equal to a given number.
In this case, the factorial of 9 is 9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 362,880.
4. Divide the factorial by the factorial of the number of times a letter is repeated. Here, we have 'I' and 'T' appearing twice.
The factorial of 2 (for 'I') is 2! = 2 × 1 = 2.
The factorial of 2 (for 'T') is also 2! = 2 × 1 = 2.
Therefore, we divide 362,880 by (2 × 2), which gives us 362,880/4 = 90,720.
Hence, there are 90,720 distinct letter words that can be made from the word "CHRISTYNA."
Since no letters repeat, this is straightforward.
number of "words" = 9! = 362880