how many 10-digit number can be made with odd digits so that no two consecutive digits are the same?
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The total possible numbers are 5*4^9
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The ten digits numbers that can be made with odd digits so that no two consecutive digits are the same are 5 × 4⁹.
The odd digits which can be considered are (1,3,5,7 and 9).
If we start from left, the first digit can be any number out of the five digits.
The second place can be filled with any four digits except the digit at the first place.
Similarly, four ways for the third digit until we reach the tenth place.
Therefore, the total numbers formed are 5 × 4⁹
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