How many distinguishable permutations of letters are possible in the word?
BASEBALL
a. 20,160 b. 10,080 c. 5040 d. 40,320
BASEBALL
8 letters = 8!
B=2,A=2,S=1,E=1,L=2
8!
_____________________ =
(2!)(2!)(1!)(1!)(2!) Using your calculator you can get the answer by following the solution above.Note,dont forget to parenthesized the denominator if you do you might get some error or you can't get the correct answer.
the answer is letter C
To find the number of distinguishable permutations of the word "BASEBALL", we need to consider the number of letters and their occurrences.
The word "BASEBALL" consists of 8 letters in total. However, some letters are repeated. Specifically, the letter 'B' appears twice, the letter 'A' appears twice, and the letter 'L' appears twice.
We can use the formula for permutations of a word with repeated letters, which is given by:
n! / (n1! * n2! * n3! * ...)
where n is the total number of letters and n1, n2, n3, etc. are the number of occurrences for each repeated letter.
So, in this case, we have:
n = 8
n1 = 2 (for 'B')
n2 = 2 (for 'A')
n3 = 2 (for 'L')
Plugging these values into the formula, we get:
8! / (2! * 2! * 2!)
Calculating this, we have:
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320
2! = 2 * 1 = 2
Substituting these values into the formula:
40,320 / (2 * 2 * 2)
Simplifying further:
40,320 / 8 = 5,040
Therefore, the correct answer is c. 5,040.
To find the number of distinguishable permutations of the letters in the word "BASEBALL," we need to determine the number of arrangements possible when all the letters are taken into account.
The word "BASEBALL" has a total of 8 letters. However, there are repeated letters, which means some arrangements may not be distinguishable from each other.
To calculate the number of distinguishable permutations, we can use the formula for permutations with repetition. The formula is given by:
n! / (m1! * m2! * ... * mk!)
Where n is the total number of objects, and m1, m2, ..., mk are the frequencies of each repeated object.
In the case of "BASEBALL," we have:
- n = 8 (total number of letters)
- m1 = 3 (the letter 'A' appears 3 times)
- m2 = 2 (the letter 'B' appears 2 times)
- m3 = 1 (the letter 'S' appears 1 time)
- m4 = 1 (the letter 'E' appears 1 time)
- m5 = 1 (the letter 'L' appears 1 time)
Now, we can substitute these values into the formula:
8! / (3! * 2! * 1! * 1! * 1!)
Calculating this expression, we get:
(8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (3 * 2 * 1 * 2 * 1 * 1) = 40,320 / 12 = 3,360
Therefore, there are 3,360 distinguishable permutations of the letters in the word "BASEBALL."
The correct option is d. 40,320.