Question 1082065: 2. Three-digit numbers are formed using the digits 0, 1, 2, 3, 4, 5 and 6. Note that a three-digit number can’t start with 0 and repetition is not allowed.
(i) How many three-digit numbers can be formed?
(ii) How many of these number are odd?
(iii) What is the probability of forming a three-digit number less than 300?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! (i) There are  sequences
of  characters that can be made with the  given digits,
without repeated characters.
However,  of those sequences would have  as its first character,
so only the other  of them are three-digit numbers.
That is  .
Calculating it a different way,
of the  3-character sequences,
 start with ,
so only  are three-digit numbers.
(ii) It is easier to start from the last digit.
For an odd three-digit number, it is necessary and also sufficient to have an odd last digit.
In the digits available,
there are odd digit choices for a last digit
that would make the three-digit number odd.
That leaves  non-zero digits left to use for a first digit.
Having used  non-zero digits for first and last digit,
you have  unused digits to use for a middle digit.
That gives you  three-digit numbers,
without repeated digits, that can be made from the given digits,
and are odd.
(iii) There are  sequences
of characters that can be made with the given digits,
without repeated characters.
The ones that are three-digit numbers less than 300 start with  or .
Only  of the 3-character sequences would have or as the first character,
so  are three-digit numbers less than 300.
That means that the probability of forming a three-digit number less than 300 is
 .
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