The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0 , $1,2,3,4,5,6,7$, such that the sum of their first and last digits should not be more than 8 , is
Solution
<p>Case I $5{ }_{---} 0$</p>
<p>Case II $5{ }_{---} 1$</p>
<p>$$
\begin{array}{ll}
5 & 2 \\
5 & 3 \\
6 & 0 \\
6 & 1 \\
6 & 2 \\
7 & 0
\end{array}$$</p>
<p>Case IX $7{ }_{---} 1$</p>
<p>$9 \times(8 \times 8 \times 8)=4608$ but 50000 is not included, so total numbers $4608-1=4607$</p>
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
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