Question 843930
 a)how many 5 digit numbers are there that exclude 0 and 7<pre>The digits that exclude 0 and 7 are {1,2,3,4,5,6,8,9}

Choose the first digit 8 ways.
Choose the second digit 8 ways.
Choose the third digit 8 ways.
Choose the fourth digit 8 ways
Choose the fifth digit 8 ways.

8×8×8×8×8 = 8<sup>5</sup> = 32768 ways.
</pre>b) How many of them start with an even number<pre>Choose the first digit 4 ways.
Choose the second digit 8 ways.
Choose the third digit 8 ways.
Choose the fourth digit 8 ways
Choose the fifth digit 8 ways.

4×8×8×8×8 = 4×8<sup>4</sup> = 4×4096 = 16384 ways.</pre>c) how many of them start and end with and even number<pre>Choose the first digit 4 ways.
Choose the second digit 8 ways.
Choose the third digit 8 ways.
Choose the fourth digit 8 ways
Choose the fifth digit 4 ways.

4×8×8×8×4 = 4×8<sup>3</sup>×4 = 4×512×4 = 8192 ways.

Edwin</pre>