Question 352524
a)  The thousands place can be filled in 2 ways (7 or 9).  After filling the thousands place, the hundreds, the tens, and the ones places can be filled in 4, 3, and 2 ways, respectively.  By the multiplication property of counting, there are
{{{2*4*3*2 = 48}}}
numbers greater than 7000.
b)  The ones place can be filled in 3 ways (2, 4, or 6).  After filling the ones place, the thousands, hundreds, and the tens places can be filled in 4, 3, and 2 ways, respectively.  By the multiplication property of counting, there are
{{{4*3*2*3 = 72}}}
even numbers.
c)  The thousands place can be filled in 2 ways (7 or 9).  The ones place can be filled in 3 ways (2, 4, or 6).  (Note that the two sets of choices are disjoint.)  The hundreds place can be filled in 3 ways, the tens place in two ways.  By the multiplication property of counting, there are
{{{2*3*2*3 = 36}}}
even numbers that are greater than 7000.

Now from the formula P(A or B) = P(A) + P(B) - P(A and B), we get
P(>7000 or even)= P(>7000)+P(even) - P(>7000 and even).
The number of ways of forming a four-digit number from 5 numbers is
{{{5*4*3*2=120}}}.
Hence P(>7000)=48/120
P(even)=72/120, and P(>7000 and even)=36/120 from
the information in the items above.
Thus, P(>7000 or even)= 48/120 + 72/120 - 36/120 = 84/120 = 7/10.