The number of different three letter arrangements that can be done from the
letters in the word "mathematics"
is; 11P3 =
11!/(11-3)! =
990
The word "BOX" consists of 3 distinct letters. The number of arrangements of these letters can be calculated using the factorial of the number of letters, which is 3! (3 factorial). Therefore, the total number of arrangements is 3! = 3 × 2 × 1 = 6. Thus, there are 6 possible arrangements of the letters in "BOX."
There are 12 two letter arrangements of the letters in PARK.
If all the letters are unique in the set, there are 6 choices for the first letter, 5 for the second letter, 4 for the third letter, etc. This results in 6 X 5 X 4 X 3 X 2 = 720 arrangements. If some of the six letters are duplicated, there will be fewer distinct arrangements.
To find the number of linear arrangements of the letters in "CALL," we need to consider the repetitions of letters. The word "CALL" has 4 letters where 'L' appears twice. The formula for arrangements of letters with repetitions is given by ( \frac{n!}{p1! \times p2! \times \ldots} ), where ( n ) is the total number of letters and ( p1, p2, \ldots ) are the frequencies of each repeated letter. Therefore, the number of arrangements is ( \frac{4!}{2!} = \frac{24}{2} = 12 ). Thus, there are 12 distinct arrangements of the letters in "CALL."
The number of 5 letter arrangements of the letters in the word DANNY is the same as the number of permutations of 5 things taken 5 at a time, which is 120. However, since the letter N is repeated once, the number of distinct permutations is one half of that, or 60.
There are 172 different arrangements.
The word "math" consists of 4 distinct letters: m, a, t, and h. To find the number of three-letter arrangements, we can use the permutation formula for selecting and arranging 3 letters from 4 distinct letters, which is given by ( P(n, r) = \frac{n!}{(n-r)!} ). Here, ( n = 4 ) and ( r = 3 ), so the calculation is ( P(4, 3) = \frac{4!}{(4-3)!} = \frac{4!}{1!} = 4 \times 3 \times 2 = 24 ). Thus, there are 24 different three-letter arrangements.
humility distinct letters
The word "Wednesday" consists of 9 letters, with the letter 'd' appearing twice. To find the number of distinct arrangements, you can 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, \ldots ) are the frequencies of the repeated letters. In this case, it is ( \frac{9!}{2!} = \frac{362880}{2} = 181440 ). Thus, there are 181,440 distinct arrangements of the letters in "Wednesday."
The number of arrangements of the letters PARTY, if the first letter must be an A is the same as the number of arrangements of the letters PRTY, and that is 4 factorial, or 24.
the arrangements occur. if there are two of the same letter then 12 all different letters then 24 three letters the same then 5 four letters the same then 1
360