The names PNM and MPN are perfectly valid. The order of the letters doesn't matter. In fact, there are 6 ways to name this plane if we just use the 3 letters. If we include "plane Z", then there are 7 total ways to name the plane.
For some reason, your teacher wants P to be the third letter as s/he mentioned MNP and NMP. But again, the order doesn't matter.
We have given the table of number of male and female contestants who did and did not win prize
The probability that a randomly selected contestant won prize given that contestant was female is
P(contestant won prize / Contestant was female)
Here we will use conditional probability formula
P(A/B) = 
Let Event A = selected contestant won prize and
event B = selected contestant is famale
Then numerator entity will
P(A and B) = P(Contestant won prize and Contestant is female)
= Number of female contestant who won prize / Total number of contestant
= 3 /(4+9+3+10)
= 3 / 26
P(A and B) = 0.1153
P(B) = P(contestant is female )
= Number of female contestant / Total number of contestants
= (3+10) / 26
P(B) = 0.5
Now P(A / B) = 
= 0.1153 / 0.5
P(A / B) = 0.2306
The probability that randomly selected contestant won prize given that contestant is female is 0.2306
Converting probability into percentage 23.06%
The percentage that randomly selected contestant won prize given that contestant is female is 23%
To get the Greates Common Factor (GCF) of 72 and 200 we need to
factor each value first and then we choose all the copies of factors and
multiply them:
<span><span>72: 22233 </span><span>200: 222 55</span><span>GCF: 222 </span></span>
The Greatest Common Factor (GCF) is: 2 x 2 x 2 = 8
Answer: 8