To find the number of permutations for each word, we can use the formula for the permutation of a word with repeating letters. The formula is:
P = n! / (n1! * n2! * ... * nk!)
where P is the total number of permutations, n is the total number of letters, and n1, n2, ..., nk are the frequencies of each repeating letter.
Let's calculate the number of permutations for each word:
1. QUEUE:
There are 5 letters in the word QUEUE. However, the letter "E" appears twice.
So the number of permutations for QUEUE is:
P = 5! / (2!)
P = 5! / 2
P = 120 / 2
P = 60
2. COMMITTEE:
There are 9 letters in the word COMMITTEE. However, the letters "M," "T," and "E" appear twice.
So the number of permutations for COMMITTEE is:
P = 9! / (2! * 2! * 2!)
P = 9! / 8
P = 362,880 / 8
P = 45,360
3. PROPOSITION:
There are 11 letters in the word PROPOSITION. However, the letters "P," "O," "I," and "N" appear twice, and the letter "S" appears thrice.
So the number of permutations for PROPOSITION is:
P = 11! / (2! * 2! * 2! * 3!)
P = 11! / (8 * 6)
P = 39,916,800 / 48
P = 832,125
4. BASEBALL:
There are 8 letters in the word BASEBALL. However, the letter "A" appears twice, and the letter "L" appears thrice.
So the number of permutations for BASEBALL is:
P = 8! / (2! * 3!)
P = 8! / (2 * 6)
P = 40,320 / 12
P = 3,360
Therefore, the number of permutations for each word are:
QUEUE: 60
COMMITTEE: 45,360
PROPOSITION: 832,125
BASEBALL: 3,360
Please note that these calculations assume all letters are distinguishable, and all possible combinations are valid permutations.