6
25 times
36 times
24 times
There are 720 possible permutations.
There are 6 letters so there are 6P6 or 720 ways to arrange them. They don't all make a real word though.
5 x 4 x 3 x 2 = 120 different ways to arrange them.
chocolate = 9 letters, where o and c are repeated 2 times. There are 9!/(2!2!) = 90,720 ways.
To find the number of distinguishable arrangements of the letters "aaabb," we use the formula for permutations of multiset: [ \frac{n!}{n_1! \times n_2!} ] where ( n ) is the total number of letters, ( n_1 ) is the number of indistinguishable letters of one type, and ( n_2 ) is the number of indistinguishable letters of another type. Here, ( n = 5 ) (total letters), ( n_1 = 3 ) (for 'a'), and ( n_2 = 2 ) (for 'b'). Calculating this gives: [ \frac{5!}{3! \times 2!} = \frac{120}{6 \times 2} = \frac{120}{12} = 10 ] Thus, there are 10 distinguishable ways to arrange the letters "aaabb."
The word "fancy" consists of 5 distinct letters. The number of ways to arrange these letters is calculated using the factorial of the number of letters, which is 5!. Therefore, the total number of arrangements is 5! = 120.
The word "banana" consists of 6 letters, with the letter "a" appearing 3 times, "n" appearing 2 times, and "b" appearing once. To find the number of unique arrangements, you can use the formula for permutations of multiset: ( \frac{n!}{n_1! \times n_2! \times n_3!} ), where ( n ) is the total number of letters, and ( n_1, n_2, n_3 ) are the counts of each distinct letter. This gives ( \frac{6!}{3! \times 2! \times 1!} = 60 ) unique arrangements of the letters in "banana."
3 times
84 times.