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.