Question 87092
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
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b) If books of the same color are to be grouped together, how many arrangements are possible?
Answer: 3! = 6
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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!]
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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
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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
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b) the telephone number must be a multiple of 10 (that is, it must end in zero)?
Answer: 10^6*1 = 100,000
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c)the telephone number must be a multiple of 100?
10^5*1*1 = 100,000
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d)the first 3 digits are 481?
Answer: 1*1*!*10^4 = 10,000
e) no repetitions are allowed?
Answer: 10C7 = 120
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Cheers,
Stan H.