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Probability Level 3

How many 10-digit numbers can be made with odd digits so that no two consecutive digits are same?

If answer is in form $A×2^{B}$ where $A$ and $B$ are positive integers and also $A$ is a prime number, find $A+B$ .

The answer is 23.

1 solution

Maria Kozlowska
Oct 16, 2016

There are 5 odd digits : $1,3,5,7,9$ . First digit of the number can be any of the 5 digits, next one can be any of the 5 digits but the first one: 4 digits, next one any of the 4 digits etc. $5 * 4^9 = 5 * 2^{18} \Rightarrow A=5, B=18, A+B=\boxed{23}$

Don't count

The answer is 23.

1 solution

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