How many 4 number combinations are the in the numbers 1 to 10?

Answer 1

First figure in combination can be any of 10, second can be any of remaining 9, third any of remaining 8 and fourth any of remaining 7 so total of possibilities is 10 x 9 x 8 x 7 ie 5040.

This assumes no repeating digits, in that case possibilities would be 10 to the fourth power ie 10000.

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The question asks for number of combinations. The above result of 5040 is the number of 4 number permutations that can be obtain from the numbers 1 to 10.

The number of different 4 number combinations that can be obtain from the numbers

1 to 10 is: 10C4 = 10!/(4!∙6!) = 210 different 4 number combinations.

If repetition of numbers in the 4 number combination are allowed we have to ad:

with 2 numbers repeated; 3∙10C3 = 3(120) = 360

with 3 numbers repeated; 2∙10C2 = 2(45) = 90

with 4 numbers repeated; 10

with two sets of 2 numbers repeated; 10C2 = 45

This gives a total of 4 number combinations with repetition of numbers allowed of:

210 + 360 + 90 + 10 + 45 = 715 different 4 number combinations.

Answer 2

Oh, that's a wonderful question! If we're looking at 4-digit combinations using the numbers 1 to 10, we can use each number more than once. So, if we have 10 options for each digit, we would have 10x10x10x10 = 10,000 possible combinations. Isn't it amazing how many beautiful possibilities there are to create something special?

Answer 3

Well, honey, if we're talking about 4-digit combinations using numbers 1 to 10, there are a total of 10,000 possible combinations. You start with 10 choices for the first digit, and since repetition is allowed, you have 10 choices for each of the remaining three digits. So, 10 x 10 x 10 x 10 equals 10,000. Math can be a real hoot when you break it down!