Question 1055966
Let,
M = Muffy
N = Nero
O = Oprah
P = Penny
Q = Quade



--------------------------------------------------------------------------------


(a)


5*4*3 = 60


There are 60 ways to do this if order mattered, but it doesn't. So we divide by 6. Why 6? Because there are 6 ways to order any 3 individuals (3! = 3*2*1 = 6). 


60/6 = 10


So the final answer to part (a) is <font color=red>10</font>. The list would be 


M,N,O
M,N,P
M,N,Q
M,O,P
M,O,Q
M,P,Q
N,O,P
N,O,Q
N,P,Q
O,P,Q


each line represents a different combination. Something like M,N,O is the same as M,O,N or N,M,O since they have the same 3 cats just in a different order. Order does not matter. As you can see in the list above, there are 10 different combinations. 


--------------------------------------------------------------------------------

(b)


Hold one slot to have it fill Oprah (O). There are 2 slots left with 4 choices to fill it


4 C 2 = (4 P 2)/(2!) = (4*3)/2 = 12/2 = 6


There are 6 ways to do this


If you look at the list in part (a), you'll see these entries that have O in them somehow


M,N,O
M,O,P
M,O,Q
N,O,P
N,O,Q
O,P,Q


There are 6 of those entries listed above. So however you do it, the final answer to part (b) is <font color=red>6</font>

--------------------------------------------------------------------------------

(c)


Look at the list in part (b). Look for entries that have both M and N together at the same time. It only happens once and it is M,N,O


The final answer to part (c) is <font color=red>1</font>

--------------------------------------------------------------------------------

(d)


In part (a), the answer is 10
In part (b), the answer is 6


There are 6 ways to get what we want (have Oprah picked) out of 10 ways total


Simply divide the two values to get


6/10 = 3/5 = 0.6


The final answer as a fraction is <font color=red>3/5</font>. Don't forget to reduce fully.

The final answer in decimal form is <font color=red>0.6</font>

The final answer as a percentage is <font color=red>60%</font>


The way you report the answer will depend on your teacher's instructions.