Question

What is the number of sequences of six digits where the number of even digits is equal to the number of odd digits?

For example, there are 50 such sequences of length two: 01, 03, 05, 07, 09, 10, 12, 14, 16, 18, ..., 90, 92, 94, 96, 98.

Answer 1

Answer:

98

Step-by-step explanation:

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Answer 2

Answer: 312500

Step-by-step explanation:

Since the digits are not required to be distinct, the 3 even digits may be allotted in 5×5×5 = 125 ways (as these are to be chosen from 0, 2, 4, 6 and 8). Similarly the odd digits can be allotted in 125 ways. Hence the required number of sequences is 20×125×125 = 312500.