using the following numbers 0,2,6,7,9 how many 4 fig numbers can you make.?

Question

Beleive it or not this is my 8 year old sons homework. PS can you list them, thats what he has to do.

Answer 1

Depends if you allow 0 as the first digit of a 4 figure number and if you allow numbers to be repeated.

Case 1, no zero at the start, but you can repeat the digits.

The first digit can be any of 4 (2, 6, 7 or 9); the second digit can be any of 5 (0, 2, 6, 7 or 9), the third any of 5 and the fourth any of 5.
Total number of possibilities: 4*5*5*5 = 500

(This is probably the answer in an 8-year-old's homework).

Case 2, no zero, and can't use the same digit twice:
1st digit, any of 4; 2nd digit any of 4 (five minus the one you used in 1st position); 3rd digit any of 3 (there are now 2 that you can't use), 4th digit any of remaining 2.
Total = 4*4*3*2 = 96

Case 3, you can use 0 as first digit and you can repeat:
Any digit can be any of 5.
Total = 5*5*5*5 = 625
(e.g., 0062 is a four-digit number, so is 0000). This is normally not considered valid unless you are into computer programming). Definitely not the type of homework for an 8-year-old.

Case 4, you can use zero in 1st position but you can't repeat:
1st is any of 5, 2nd is any of remaining 4, etc.
Total = 5*4*3*2 = 120

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For an 8-year-old, take Case 1.