Question

Dafes stickball team has six players.how many different six player battling lineups can they make ifdave must bat second and either zack or paul must bat first

Answer 1

Let us name the players A,Dave,Zack,Paul,E and F 
For the first position there are two candidades ( Zack / Paul ) 
For the second position there is only one candidate i.e. Dave 
For the third place there will be 4 candidates (out of Zack and Paul - 1 as one of them is already taken for the first position and A, E and F total-4) 
For the fourth place there will be 3 candidates ( out of the four available candidates in the 3rd place, one will be taken up for 3rd place ) 
For the fifth place there will be 2 candidates 
Finally, for the last place there will be only one candidate left. 
On multiplying the no. of available cadidates, we get 2 * 1 * 4 * 3 * 2 * 1 = 48 i.e. option (A) 
Please mention minor spelling mistakes 
For the second question: 
Let the no of dotted marbles be 'x' and no of striped marbles be 'y' 
then the equation will become as follows 
(y+6)/x = 3 
and 
(x+6)/y = (2/3) 
On solving the equations, we will get x = 10 and y = 24 
Total balls = 10+24+6 = 40 (option E) 
Answer 3 will be ) For the first edge, he can choose 3 paths 
For the second edge he can choose 2 paths for each path of its first edge's path 
For the third , he is bounded to move on the paths created by the first and the second edges hence 1 path for each path created by the first and the second edge together 
It will be multiplication of all the possibilities of the paths of the three edges differently......... 
i.e. 3 * 2 * 1 = 6