Answered

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How many sequences of 6 digits $x_1, x_2, \ldots, x_6$ can we form, given the condition that no two adjacent $x_i$ have the same parity

Sagot :

MrRoyal

The parity of each digit represents if the digit is even or odd

There are 31250 sequence of 6 digits that can be formed

How to determine the sequence of digits

The 6 digit is given as: x1 x2 x3 x4 x5 x6

For no two adjacent numbers to have the same parity (i.e. adjacent numbers cannot be both odd or even), the following must be true

  • x1 can be any of the 10 digits
  • x2 to x6 can be any of 5 even/odd digit from 0 to 9 (this depends on the parity of x1)

So, the total sequence of digits is:

[tex]Total = 10 * 5 * 5 * 5 * 5 * 5[/tex]

Evaluate the products

[tex]Total = 31250[/tex]

Hence, there are 31250 sequence of 6 digits that can be formed

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