The number of permutations of 8 distinct things is given by 8 factorial, denoted as 8!. This is calculated as 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1, which equals 40,320. Therefore, there are 40,320 permutations of 8 distinct items.
There are 9 * 8 * 7, or 504, three letter permutations that can be made from the letters in the work CLIPBOARD.
Since there are no duplicate letters in the word RAINBOW, the number of permutations of those letters is simply the number of permutations of 7 things taken 7 at a time, i.e. 7 factorial, which is 5040.
3x2x1=6 permutations.
The word "algrebra" has 8 letters, with the letter 'a' appearing twice and 'r' appearing twice. To find the number of distinguishable permutations, we use the formula for permutations of multiset: ( \frac{n!}{n_1! \times n_2!} ), where ( n ) is the total number of letters and ( n_1, n_2 ) are the frequencies of the repeating letters. Thus, the number of distinguishable permutations is ( \frac{8!}{2! \times 2!} = 10080 ). Since all letters are counted in this formula, there are no indistinguishable permutations in this context.
There are 195 3-letter permutations.
There are 8! = 40320 permutations.
There are 8 letters in "geometry", so there are 8! (factorial) ways to arrange them in different permutations. 8! = 40,320 permutations.
If they are all different, then 40320.
Since the word MATH does not have any duplicated letters, the number of permutations of those letters is simply the number of permutations of 4 things taken 4 at a time, or 4 factorial, or 24.
The word MATHEMATICS has 11 letters. The number of permutations of 11 things taken 11 at a time is 11 factorial (11!), or 39,916,800.
There are 9 * 8 * 7, or 504, three letter permutations that can be made from the letters in the work CLIPBOARD.
Since there are no duplicate letters in the word RAINBOW, the number of permutations of those letters is simply the number of permutations of 7 things taken 7 at a time, i.e. 7 factorial, which is 5040.
The number of permutations of the letters SWIMMING is 8 factorial or 40,320. The number of distinct permutations, however, due to the duplication of the letters I and M is a factor of 4 less than that, or 10,080.
geometry has 8 letters, 2 of which are the same (e) So, the answer is 8!/2! = 20,160
8 digits will generate over 40,000 permutations.
3x2x1=6 permutations.
LOLLIPOP = 8 letters L=3 O=2 I=1 P=2 number of permutations = 8!/3!2!2! = 8x7x6x5x4x3x2 / 3x2x2x2 = 40320 /24 = 1680