Respuesta :
Answer:
The number of ways in which the word "balloon" can be arranged is 1260
Step-by-step explanation:
The given word is "balloon: The word has 7 letters.
We know that n different things can be arranged in n! ways.
Hence, 7 different things can be arranged in 7! ways.
Now, in the word"balloon" the characters "l" and "o" repeats twice. Hence, these can be arranged themselves in 2! ways. Hence, we have to divide 7! by (2!2!).
Therefore, the number of ways in which the word "balloon" can be arranged is
[tex]\frac{7!}{2!2!}\\\\=1260[/tex]
Total number of letters in the word "BALLOON" is 7 and letter 'O' and letter 'L' occurs two times.The number ways can the letters in the word balloon be arranged is 1260. Thus the option B is the correct option.
What is arrangement?
Arrangement of the things or object is mean to make the group of them in a systematic order, in all the possible ways.
The number of possible ways to arrange is the n!.
Here, n is the number of objects.
Given information-
The word which is given to arrange is 'BALLOON"
Total number of letters in the given word is 7.
In the given word, letter 'O' and letter 'L' occurs two times.
As there is total 7 letter in the given word. Thus the number of arrangement should be, 7! ways.
As the letter 'O' and letter 'L' occurs two times, thus the number arrangement should be divided with (2!2!).
Thus, the number ways can the letters in the word balloon be arranged is,
[tex]P=\dfrac{7!}{2!\times2!} \\P=\dfrac{7\times6\times5\times4\times3\times2!}{2!\times2\times1}\\P=1260[/tex]
Hence, the number ways can the letters in the word balloon be arranged is 1260. Thus the option B is the correct option.
Learn more about the arrangement here;
https://brainly.com/question/6032811
