123, 124, 125, 132, 134, 135, 142, 143, 145, 152, 153, 154
213, 214, 215, 231, 234, 235, 241, 243, 245, 251, 253, 254
312, 314, 315, 321, 324, 325, 341, 342, 345, 351, 352, 354
412, 413, 415, 421, 423, 425, 431, 432, 435, 451, 452, 453
512, 513, 514, 521, 523, 524, 531, 532, 534, 541, 542, 543
A total of sixty combinations.
You could also use the Permutation formula with no repetition to get the result, without having to list them all out. This is important once you start getting into higher numbers.
The formula is n! / (n-r)! where n is the total number of items, and r is the number of items you are taking for each permutation.
The exclamation (!) means factorial. You take n * (n-1) * (n-2) * (n-3) * . . . . * 1.
In this case n=5 and r=3
so 5! / (5-3)! = (5 * 4 * 3 * 2 * 1) / (2 * 1) = 120/2 = 60. I'm posting a link for more information.
137, 173, 317, 371, 713, 731 Six combinations can be made.
35
In a 7 segment display, the symbols can be created using a selected number of segments where each segment is treated as a different element.When 1 segment is used, the possible positions are 7because it can be any of the 7 segments (7C1=7).When 2 segments are used, the number of possible combinations are 7C2=21.When 3 segments are used, the number of possible combinations are 7C3=35When 4 segments are used, the number of possible combinations are 7C4=35When 5 segments are used, the number of possible combinations are 7C5=21When 6 segments are used, the number of possible combinations are 7C6=7When 7 segments are used, the number of possible combinations are 7C7=1Adding the combinations, 7+21+35+21+7+1=127Therefore, 127 symbols can be made using a 7 segment display!
Using the combination fuction, chose three numbers from 45 numbers. The answer is 14,190.
720
137, 173, 317, 371, 713, 731 Six combinations can be made.
Assuming you are using the standard English alphabet, the number of combinations you can make are: 26 x 26 = 676 combinations.
4
1000
35
There are countless possible liquid combinations, depending on the types of liquids you are considering (water, juice, alcohol, etc.) and how many you want to mix together. The number of combinations would be exponential, as each additional liquid increases the number of possible combinations exponentially.
In a 7 segment display, the symbols can be created using a selected number of segments where each segment is treated as a different element.When 1 segment is used, the possible positions are 7because it can be any of the 7 segments (7C1=7).When 2 segments are used, the number of possible combinations are 7C2=21.When 3 segments are used, the number of possible combinations are 7C3=35When 4 segments are used, the number of possible combinations are 7C4=35When 5 segments are used, the number of possible combinations are 7C5=21When 6 segments are used, the number of possible combinations are 7C6=7When 7 segments are used, the number of possible combinations are 7C7=1Adding the combinations, 7+21+35+21+7+1=127Therefore, 127 symbols can be made using a 7 segment display!
9
Using the combination fuction, chose three numbers from 45 numbers. The answer is 14,190.
720
You can make 5 combinations of 1 number, 10 combinations of 2 numbers, 10 combinations of 3 numbers, 5 combinations of 4 numbers, and 1 combinations of 5 number. 31 in all.
The question is incorrect since there are 210 - 1 possible combinations. The digit 0 can be in the combination or out. That gives 2 ways. With each, the digit 1 can be in the combination or out - 2*2 = 22 ways. With each, the digit 2 can be in the combination or out = 23 ways. With each, the digit 3 can be in the combination or out = 24 ways. etc. So 210 ways in all except that one of them is the null combination. Now 210 = 1024 so there are only 1023 combinations. If, instead, you allow the digits to be used many times, there is no limit to the number of combinations.