how many odd four-digit numbers

[wind]

how many odd four-digit numbers, all of the digits different, can be formed from the digits 0 to 7, if there must be a 4 in the number?

7*7*1*4

7b/c 0 cant be first
7 b/c no repeting
1 b/c it has to be 4
4 b/c it has to be odd

Is this right?

Thanks

 

[pka]

I get many more than that.

Because they are to be odd, begin with choosing the ones’ digit: 4 choices.

The number must contain the digit 4, so consider two cases.
If the thousandth digit is a 4 we can choose the hundredth digit in 6 ways and the tens digit in 5 ways.

If the thousandth digit is not 4 we can choose the thousandth digit in 5 ways. We have two choices where to put the 4 and the other digit in 5 ways.

ANS: (6)(5)(4)+(5)(2)(5)(4).

 

[wind]

thanks Pka