There are just 5,005.There are 10C6 = 210 combinations with 6 different numbers.There are 10C5 = 252 combinations with 5 different numbers. One of these needs to be duplicated and the one to be duplicated can be chosen in 5 ways so there are 1260 of these.There are 10C4 = 210 combinations with 4 different numbers. Either one of them appears three times or two are doubled. That can be done in 10 ways so there are 2,100 of these.There are 10C3 = 120 combinations with 3 different numbers. Either one of them appears 4 times, or one twice and another three times, or all three appear twice. That can be done in 10 ways so there are 1,200 of these.There are 10C2 = 45 combinations with 2 different numbers. Either one of them appears 5 times, or one twice and another four times, or both three times. That can be done in 5 ways so there are 225 of these.There are 10C1 = 10 combinations with just 1 number repeated six times.Add these together.
-.45 is rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
We are looking for all sets with an odd number of elements in them. To find this we can use combinations. Adding up the odd combinations will total the subsets containing an odd number of elements.nCr where n=10 and r=(1,3,5,7,9)10C1 + 10C3 + 10C5 + 10C7 + 10C9 = 512.You could also take the total number of elements (2^10) and subtract all sets containing an even number of elements.nCr where n=10 and r=(0,2,4,6,8,10)1024-(1+45+210+210+45+1)=512
10C2 = 45
Once you put the numbers in order, the median is the middle number or the average of the 2 middle numbers. 13, 19, 39, 44, 45, 58, 68. 44 is the number in the middle, so 44 is the median.
Number of combinations = 45C6 = 45!/6!(45-6)! = 8,145,060
There are 45 combinations.
Could you generate a complete set of 6 number combinations from 45 numbers ?
Using the combination fuction, chose three numbers from 45 numbers. The answer is 14,190.
About 13million,
This is a Permutation problem; nPr. This is: n!/(n-r)! or 45!/(45-5)! = 146611080.
Any 6 from 45 = 814506045C6 = 8145060
45*44*43*42/(4*3*2*1) = 148995
There is 1 combination of all ten numbers, 10 combinations of one number and of nine numbers, 45 combinations of two or eight numbers, 120 combinations of three or seven numbers, 210 combinations of four or six numbers and 252 combinations of five numbers. That is 1023 = 210 - 1 in total.
45.
45
There are 10 combinations of 1 number,10*9/(2*1) = 45 combinations of 2 numbers,10*9*8/(3*2*1) = 120 combinations of 3 numbers,10*9*8*7/(4*3*2*1) = 210 combinations of 4 numbers,10*9*8*7*6/(5*4*3*2*1) = 252 combinations of 5 numbers,210 combinations of 6 numbers,120 combinations of 7 numbers,45 combinations of 8 numbers,10 combinations of 9 numbers, and1 combination of 10 numbers.All in all, 210 - 1 = 1023 combinations. I have neither the time nor inclination to list them all.There are 10 combinations of 1 number,10*9/(2*1) = 45 combinations of 2 numbers,10*9*8/(3*2*1) = 120 combinations of 3 numbers,10*9*8*7/(4*3*2*1) = 210 combinations of 4 numbers,10*9*8*7*6/(5*4*3*2*1) = 252 combinations of 5 numbers,210 combinations of 6 numbers,120 combinations of 7 numbers,45 combinations of 8 numbers,10 combinations of 9 numbers, and1 combination of 10 numbers.All in all, 210 - 1 = 1023 combinations. I have neither the time nor inclination to list them all.There are 10 combinations of 1 number,10*9/(2*1) = 45 combinations of 2 numbers,10*9*8/(3*2*1) = 120 combinations of 3 numbers,10*9*8*7/(4*3*2*1) = 210 combinations of 4 numbers,10*9*8*7*6/(5*4*3*2*1) = 252 combinations of 5 numbers,210 combinations of 6 numbers,120 combinations of 7 numbers,45 combinations of 8 numbers,10 combinations of 9 numbers, and1 combination of 10 numbers.All in all, 210 - 1 = 1023 combinations. I have neither the time nor inclination to list them all.There are 10 combinations of 1 number,10*9/(2*1) = 45 combinations of 2 numbers,10*9*8/(3*2*1) = 120 combinations of 3 numbers,10*9*8*7/(4*3*2*1) = 210 combinations of 4 numbers,10*9*8*7*6/(5*4*3*2*1) = 252 combinations of 5 numbers,210 combinations of 6 numbers,120 combinations of 7 numbers,45 combinations of 8 numbers,10 combinations of 9 numbers, and1 combination of 10 numbers.All in all, 210 - 1 = 1023 combinations. I have neither the time nor inclination to list them all.