Problem 49
Question
Find the number of distinguishable permutations of the group of letters. \(\mathbf{A}, \mathbf{L}, \mathbf{G}, \mathbf{E}, \mathbf{B}, \mathbf{R}, \mathbf{A}\)
Step-by-Step Solution
Verified Answer
The number of distinguishable permutations of the group of letters is 2520.
1Step 1: Count the total number of characters
Count the total number of letters in the set to find the value of 'n'. In this case, the group contains 7 letters, so n=7.
2Step 2: Identify repeating characters
Identify any characters that repeat in the group. Here, 'A' is repeated twice, so its repetitions will be considered as p1=2. All other letters occur only once, so they aren't considered as repetitions.
3Step 3: Apply the formula of permutation with repetition
Apply the formula for calculating permutations taking repetitions into account. The formula is n! / p1!*p2!*...*pk!. In this case, it would be 7! / 2! = 5040 / 2. Therefore, the number of distinguishable permutations of the given group of letters is 2520.
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