Answer:
Step-by-step explanation:
1. Number of boys in the group = 25
Number of girls in the group = 18
Total children = 25 + 18 = 43
Number of ways to arrange the children in a way = 43!
2. If we consider all the boys as an individual then number of ways children can be arranged = 19!
Number of ways boys can sit next to each other = 25!
So the number of ways can be arranged = 19!×25!
3. Number of ways boys can sit next to each other = 25!
Number of ways girls can sit next to each other = 19!
Then number of ways to arrange the children in a row with all boys next to each other and all the girls next to each other will be = 2 × 18! × 25!
4. 1. To choose a chess team if anyone can be chosen
= 
= 6096454
4. 2. Exactly 2 girls must be chosen then number of ways
= 
4. 3. At least two boys must be chosen
= 
= 5863690
<span>The fact that Helen’s indifference curves touch the axes should immediately make you want to check for a corner point solution. To see the corner point optimum algebraically, notice if there was an interior solution, the tangency condition implies (S + 10)/(C +10) = 3, or S = 3C + 20. Combining this with the budget constraint, 9C + 3S = 30, we find that the optimal number of CDs would be given by 3018â’=Cwhich implies a negative number of CDs. Since it’s impossible to purchase a negative amount of something, our assumption that there was an interior solution must be false. Instead, the optimum will consist of C = 0 and Helen spending all her income on sandwiches: S = 10. Graphically, the corner optimum is reflected in the fact that the slope of the budget line is steeper than that of the indifference curve, even when C = 0. Specifically, note that at (C, S) = (0, 10) we have P C / P S = 3 > MRS C,S = 2. Thus, even at the corner point, the marginal utility per dollar spent on CDs is lower than on sandwiches. However, since she is already at a corner point with C = 0, she cannot give up any more CDs. Therefore the best Helen can do is to spend all her income on sandwiches: ( C , S ) = (0, 10). [Note: At the other corner with S = 0 and C = 3.3, P C / P S = 3 > MRS C,S = 0.75. Thus, Helen would prefer to buy more sandwiches and less CDs, which is of course entirely feasible at this corner point. Thus the S = 0 corner cannot be an optimum]</span>
D . Y=2x-3kdmdkdmdmdmdmxkx
ans is b...multiply first eqn by -2
=》 -6x -4y = -48...eqn 3
add eqn 2 and 3...
=》 -2y = -18
=》 y = 9...x =2
