Preputation , 有答案, 只想要解釋

(a)
The first place cannot place the digit 0
(for example 01234 does not accept)
so, we have 5 choice
At the second place, we have 5 choice
the third place, 4 choice
the fourth place, 3 choice
the fifth place, 2 choice
Total different integers can be formed
=5*5*4*3*2
=5*5P4
=600
(b)
For 5 digits odd number
the fifth digit should be odd, we have three choice (1,3,5)
let say the fifth place is 1
then
At the first place, we have 4 choice
At the second place, we have 4 choice
the third place, 3 choice
the fourth place, 2 choice
So the different integers can be formed that the last digit is 1
=4*4*3*2
=4*4P3
the same argument can be used for last digit 3 and 5
so
the total different integers can be formed
=4x 4P3 x 3
=288