There are eight (8) different letters in that word, so that's the number of
letter choices you have in each 5-letter group without repetition.
The number of different 5-letter "words" is (8 x 7 x 6 x 5 x 4) = 6,720 .
(They don't necessarily mean anything. They're just distinct sequences
of 5-letters each, like Morse-code random practice groups.)
There are 2000 such numbers.
if the repetition is allowed the there is 6*6*6 possible ways = 216
9 odd numbers less than 100 can be formed. They are: 3,5,7,35,37,53,57,73 and 75.
If repetition is allowed and leading zeros are allowed, then you have 000 to 999, which is 1,000 possibilities (I will not list them here). If no leading zeros are allowed, then you have 100 through 999, so there are 900 possibilities. If there are other restrictions, such as no repetition, then I'll refer you to the related link at MathsIsFun.com
If the first number can not be zero then it is 9x9x8x7x6=27,216 If the first number can be zero then it would be 10x9x8x7x6=41,160
It is 720.
If repetition is allowed . . . . . 343 If repetition is not allowed . . . . . 210
64 if repetition is allowed.24 if repetition is not allowed.
64 if repetition is allowed, 6 otherwise.64 if repetition is allowed, 6 otherwise.64 if repetition is allowed, 6 otherwise.64 if repetition is allowed, 6 otherwise.
In a set, as it is usually defined, elements can't be repeated. "Mathematics" has 8 distinct letters, so your set would have 8 letters. The number of possible subsets (this includes the empty set, and the set itself) is two to the power 8.
If repetition of digits isn't allowed, then no13-digit sequencescan be formed from only 5 digits.
There are 2000 such numbers.
There are 5*5*5 = 125 such numbers.
if the repetition is allowed the there is 6*6*6 possible ways = 216
125 There are five choices for each of the three digits (since repetition is allowed). So there are 5*5*5=125 combinations.
It is 415968.
125