Question

Using the digits 3, 4, 5, 6, 7, 8, and 9, how many 5-digit numbers can be constructed if the number must begin with an odd digit and digits may not be repeated?

Answer 1

You have five spaces to fill.
The first space can only be filled with odd numbers, of which there are four possibilities.
The next space can be filled with one of six possibilities. (Seven, minus the one number you already used.)
The third space has five possibillities.
The fourth space has four possibilities left.
The last space has three.
So: 4*6*5*4*3 = 1140

Answer 2

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