The number of different 4-digit strings is 6*5*4*3 = 360
120 There are 6 digits in total. The numbers with 3 digits, with all digits distinct from each other, are the permutations of the 6 digits taken 3 at a time, and therefore there are 6*5*4 = 120 of them.
Assuming that the first digit can't be zero: If repetition of digits is permitted: (5 x 6 x 6) = 180 numbers of 3 digits. If repetition of digits is not permitted: (5 x 5 x 4) = 100 numbers of 3 digits.
30 without repetition (6P2) 66 with repetition (12C2)
36
There are 10 numbers in all including 0. The first space can be filled in 9 ways (as we have to exclude 0). The second through sixth spaces can be filled in 10 ways as 0 can be included. Totally, 9 x 10 x 10 x 10 x 10 x 10 or 9 x 10^5 digits can be formed if repetition is allowed.
64 if repetition is allowed.24 if repetition is not allowed.
If repetition of digits isn't allowed, then no13-digit sequencescan be formed from only 5 digits.
15 of them.
125
There are 2000 such numbers.
Six (6)
I take it that you want to make three digits numbers with 8,7,3, and 6 without repetition. The first digit cane be selected from among 4 digits, the second from 3 digits, the third digit from 2, hence the number of three digit numbers that can be formed without repetition is 4 x 3 x 2 = 24
Possible solutions - using your rules are:- 11,13,17,31,33,37,71,73 &77
There are 2000 such numbers.
9*8*7 = 504 of them.
3*2*1 = 6 of them.
9 odd numbers less than 100 can be formed. They are: 3,5,7,35,37,53,57,73 and 75.