- #1
paulmdrdo1
- 385
- 0
How many 3 digit even numbers can be formed from 0, 1, 2, 3, 4, 5 and 6 with no repetition?
My attempt:
$\frac{5}{H} \times \frac{6}{T} \frac{0}{U} = $ 30 numbers ending with zero not including two digit numbers starting with zero$\frac{4}{H} \times \frac{6}{T} \frac{2}{U} = $ 24 numbers ending with two not including two digit numbers starting with zero$\frac{4}{H} \times \frac{6}{T} \frac{4}{U} = $ 24 numbers ending with four not including two digit numbers starting with zero$\frac{4}{H} \times \frac{6}{T} \frac{6}{U} = $ 24 numbers ending with 6 not including two digit numbers starting with zero
$\therefore$ $30+72= 102$ three-digit even numbers. But in the book's answer key it says 105. What went wrong in my solution? Please help.
My attempt:
$\frac{5}{H} \times \frac{6}{T} \frac{0}{U} = $ 30 numbers ending with zero not including two digit numbers starting with zero$\frac{4}{H} \times \frac{6}{T} \frac{2}{U} = $ 24 numbers ending with two not including two digit numbers starting with zero$\frac{4}{H} \times \frac{6}{T} \frac{4}{U} = $ 24 numbers ending with four not including two digit numbers starting with zero$\frac{4}{H} \times \frac{6}{T} \frac{6}{U} = $ 24 numbers ending with 6 not including two digit numbers starting with zero
$\therefore$ $30+72= 102$ three-digit even numbers. But in the book's answer key it says 105. What went wrong in my solution? Please help.