SOLUTION: I need help with these two problems can someone help me, I know they are long but i am in a big "?" ......thanks Problem #1 Wind has different books to arrange on a shelf: 4 bl

Question 87092: I need help with these two problems can someone help me, I know they are long but i am in a big "?" ......thanks
Problem #1
Wind has different books to arrange on a shelf: 4 blue, 3 green, and 2 red.
a) In how many ways can the books be arranges on a shelf?
b) If books of hte same color are to be grouped together, how many arrangements are possible?
c) In how many distinguishable ways can the books be arranged inf books of the same color are indentical but need not to be grouped together?
d) In how many ways can you select 3 books , one of each color, if the order in which the books are selected does not matter?

Problem #2
How many 7-digit telephone numbers are possible if the first digit cannot be zero and
a) only odd digits may be used?
b) the telephone number must be a multiple of 10 (that is, it must end in zero)?
c)the telephone number must be a multiple of 100?
d)the first 3 digits are 481?
e) no repetitions are allowed?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Problem #1
Wind has different books to arrange on a shelf: 4 blue, 3 green, and 2 red.
a) In how many ways can the books be arranged on a shelf?
Answer: 9! = 362880
------------------------------
b) If books of the same color are to be grouped together, how many arrangements are possible?
Answer: 3! = 6
---------------------
c) In how many distinguishable ways can the books be arranged if books of the same color are indentical but need not to be grouped together?
Answer: 9!/[4!*3!*2!]
------------------------------
d) In how many ways can you select 3 books , one of each color, if the order in which the books are selected does not matter?
Answer: 4*3*2 = 24
-----------------------------
Problem #2
How many 7-digit telephone numbers are possible if the first digit cannot be zero and
a) only odd digits may be used?
Answer: 5^7 = 8125
----------------
b) the telephone number must be a multiple of 10 (that is, it must end in zero)?
Answer: 10^6*1 = 100,000
---------------------------
c)the telephone number must be a multiple of 100?
10^5*1*1 = 100,000
------------------------
d)the first 3 digits are 481?
Answer: 1*1*!*10^4 = 10,000
e) no repetitions are allowed?
Answer: 10C7 = 120
-----------------------
Cheers,
Stan H.

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