1. Train B leaves P for Q, 240 miles away, one hour after Train A. In two hours, Train B reaches a point that Train A had passed 45 minutes earlier. B’s rate was then increased by 5 miles per hour, and the trains arrived at Q at the same time. Find the rate at which each train started.

2. What is the probability that there will be a majority of men on a committee of three, chosen by lot from 5 men and 3 women?

3. If 4 dimes and 3 nickels are placed at random in a straight line, what is the chance that the coins at both ends will both be nickels?

4. If all the 4-letter combinations possible are made from the alphabet (no letter used more than once in any combination), what is the chance that x is in any combination chosen at random?

5. In how many ways can 3 coins be given away if there are 6 possible recipients.

6. A gives B twice as much as C has. Then, B gives C one-third as much as A has. C then gives A one-half as much as A has. B then gives C $8 more than C has. B’s and C’s amounts are equal, and A has $36. How much did they have to begin with if A could have given C $12 and C’s amount would be equal to B’s?