how many combinations of 4 numbers can be made from the set of numbers {2, 4, 6, 7, 8, 9}?

Answer 1

They are all different digits and the order of the selection is important.

Answer P(6,4) = 6! / 2! = 360

Answer 2

It depends on what you are looking for. The term "combination" has a very specific mathematical definintion. It means that you want groups of items, the order of which doesn't matter. In other words, in this case, if you had 2, 4, 6, and 7 as a group, it would be equivalent to 4, 6, 7, 2, and both would be counted as a single grouping. If order mattered, then these would be separate groupings, and they would be permutations, not combinations. I'll give the method for both permutations and combinations.

So, if order matters, then you use the permutation calculation xPy = x!/(x-y)! or in this case:

6P4 = 6!/(6-4)! = 6!/2! = 6*5*4*3 = 360

If you are really looking for combinations (where order doesn't matter), then you use the combination formula:

xCy = x!/(y!(x-y)!) or in this case:

6C4 = 6!/4!2! = 6*5*4*3*2/4*3*2*2 = 3*5 = 15

Answer 3

there are 6 numbers and each one can be used in any position as many times in the 4 digit number.

assumptions: order does matter and any digit can be repeated.

so we get 6*6*6*6 = 1296 different numbers with any of the digits being able to be repeated..

if digits cant be repeated it becomes 6*5*4*3 = 360.

and if order is not important and you just want groups of 4 numbers regardless of order then we get:
6C4 = 6!/4!2! = 6*5/2 = 15

the qestion is a little vague so it is not clear which method you are going for.

Answer 4

probability and statistics is used here. if you want the combinations and the numbers could be repeating, then the formula should be
P(6,4)=6*6*6*6 = 6^4 = 1296.

but if the numbers cannot repeat, then the formula should be
P(6,4)=6*5*4*3 = 360.

you could also use the probability function on your scientific calculator, if you have one. :)

Answer 5

6*5*4*3*2*1 / 4*3*2*1 = 6*5 = 30
theres a button on your calculator to do this! 6Pr4 where 6 is the total number of combinations and 4 is the number you want to pick

Answer 6

6^4=1296

Answer 7

Combinations = n!/(r!(n-r)!) or n things taken r at a time.


c = 6!/(2!(6-4)!)

c = 6!/(2!(2)!) = 720/4

c = 180
.

Answer 8

6x5x4x3

but if the numbers can be used more than once, then

6x6x6x6