instruction:
In this task, you need to provide the correct option for a given problem on probability from the provided options.
question:
Problem: a question paper has 2 parts , a & b , each containing 10 questions . if a student has to choose 8 from part a & 5 from part b , in how many ways can he choose the questions ? 
Options: a ) 1100 , b ) 1200 , c ) 1235 , d ) 1354 , e ) 1140
answer:
e


question:
Problem: x , y , and z are all unique numbers . if x is chosen randomly from the set { 8 , 9 , 10 , 11 } and y and z are chosen randomly from the set { 20 , 21 , 22 , 23 } , what is the probability that x and y are prime and z is not ? 
Options: a ) 1 / 16 , b ) 3 / 11 , c ) 13 / 20 , d ) 3 / 10 , e ) 1 / 10
answer:
a


question:
Problem: in how many ways 6 boys and 4 girls can be seated in a row so that they are alternative ? 
Options: a ) 14420 , b ) 12620 , c ) 17280 , d ) 21200 , e ) 24560
answer:

c