How many three-letter code words can be constructed from the first ten letters of the Greek alphabet if no repetitions are allowed?
different code words
Answers
Answer:
10*9*8=720 ANSWER.
Explanation:
Answer:
A total of, 720 ways, in which three-letter code words can be constructed from the first ten letters of the Greek alphabet when no repetitions are allowed
Explanation:
In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set.
Now consider the given question,
Here we have the first 10 letters of English alphabet, and need to find the number of ways where the 3 letters code can be formed without repeating any letters.
There are 10 letters of English alphabet.
As we know that repetition of the letters is not allowed,
so, the first place can be filled by any of 10 letters.
Second place can be filled with any of the remaining 9 letters.
The third place can be filled with any of the remaining 8 letters.
Therefore, Number of 3-letter code can be formed when the repetition of letters is not allowed
⇒10×9×8
On multiplication, we get
∴720ways
Therefore a total of 720 ways is possible.
Note: We can also find these type of question by directly using the permutation formula i.e., nPr=n!(n−r)!
, Here, “nPr
” represents the “r” objects to be selected from “n” objects without repetition, in which the order matters.
In the given question we have taken 3 letters to be selected from 10 letters without repetition, then by formula
⇒10P3=10!(10−3)!
⇒10!7!
⇒10×9×8×7!7!
On simplification, we get
∴720ways
For more such question: https://brainly.in/question/3116555
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