Take note of the word "surprising":
There are 10! total ways to arrange the letters. Since repetition is not allowed for the arrangements, we need to divide the total number of arrangements by 2!2!2! Therefore, you should get 10!/(2!2!2!) distinct arrangements
The number of distinct arrangements of the letters of the word BOXING is the same as the number of permutations of 6 things taken 6 at a time. This is 6 factorial, which is 720. Since there are no duplicated letters in the word, there is no need to divide by any factor.
6! = 6x5x4x3x2x1 = 720 arrangements
6! =720
120.
432
There are 6!/(3!*2!) = 60 arrangements.
The word "NUMBER" consists of 6 distinct letters. The number of different arrangements of these letters can be calculated using the factorial of the number of letters, which is 6!. Therefore, the total number of arrangements is 6! = 720.
There are 34650 distinct orders.There are 34650 distinct orders.There are 34650 distinct orders.There are 34650 distinct orders.
The number of distinct arrangements of the letters of the word BOXING is the same as the number of permutations of 6 things taken 6 at a time. This is 6 factorial, which is 720. Since there are no duplicated letters in the word, there is no need to divide by any factor.
The word "college" has 7 letters, including 2 'l's and 2 'g's, which are repeated. To find the number of distinct arrangements, we use the formula for permutations of multiset: [ \frac{n!}{n_1! \cdot n_2!} ] where (n) is the total number of letters, and (n_1), (n_2) are the frequencies of the repeated letters. Here, (n = 7), (n_1 = 2) (for 'l'), and (n_2 = 2) (for 'g'): [ \text{Distinct arrangements} = \frac{7!}{2! \cdot 2!} = \frac{5040}{4} = 1260. ] Thus, there are 1,260 distinct arrangements of the letters in "college."
The word "spineless" has 9 letters, including 3 s's and 2 e's, so the number of distinct permutations of the letters is: 9!/(3!2!) = 30,240
There are 12 two letter arrangements of the letters in PARK.
6! = 6x5x4x3x2x1 = 720 arrangements
There are 6! = 720 different arrangements.
64 different arrangements are possible.
There are 4 letters in IOWA, all non repeating. Arrangements are 4! or 24.
There are 5!/2! = 60 arrangements.