SOLUTION: 1. 4 DIFFERENT math books and 5 DIFFERENT science books are to be arranged on a shelf. How many possible arrangements can be made if: a.the books on the same subject are to be arr

Question 1073432: 1. 4 DIFFERENT math books and 5 DIFFERENT science books are to be arranged on a shelf. How many possible arrangements can be made if:
a.the books on the same subject are to be arrange together?
b.the books are to be arranged alternately
Pls understand that it says that it is DIFFERENT books.. Please help me because I can't solve it..
2.There are 4 commuter trains and 5 express busses departing from towns A and B in the morning and 3 commuter trains and 4 express busses operating on the return trip in the evening. In how many ways can a commuter from towns A and Towns B complete a daily round trip via bus or train
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Note that arrangements are permutations
:
(1.a) 4! * 5! * 2! = 24 * 120 * 2 = 5760 possible arrangements
:
consider the math books and science books as two distinct entities, then you have 2! ways to arrange those two entities
:
(1.b) arrange the science books first, we have
:
5 m 4 m 3 m 2 m 1
:
next arrange the math books
:
5 4 4 3 3 2 2 1 1 = 2880 possible arrangements
:

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