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The number of ways 4 digit numbers can be forms using the digits 0 to 9 with no number repeated is given by
The probability that one of the numbers is 9876 is given by
The probability that one of the numbers is 9876 is given by
has critical points where
:
where is any integer. We get solutions in the interval
for
, for which
.
At this critical point, we have .
At the endpoints of the given interval, we have and
.
So we have the extreme values