I received the following question as part of my Discrete Mathematics course and am unable to solve it.
How many strings of four decimal digits that do not contain the same digit three times?
I know that it is related to counting rules and involves the product and sum rules however, I can not decide what approach to take to solve.
What I have so far: 1) Solution 1 Total number of combinations = 10 * 10 * 10 * 10 = 10 ^ 4 = 10 000
Number of combinations where the string contains the same digit three times: 1 * 1 * 1 * 10 = 10 * 10 (since 0 - 9 are possible numbers that can be repeated) = 100
Number of combinations where the string does not contain the same digit three times: 10 000 - 100 = 9 900
Help Needed: I do not know if this is correct. If it isn't, I would be very appreciative if someone could direct me to the correct method for solving the problem.