Question 77975This question is from textbook college algebra
: Can you please help me with this problem?
How many 7-digit telephone numbers are possible if the first digit cannot be 0 and
(a) only odd digits may be used?
(b) the telephone number must be a multiple of 10, (that is, it must end in 0)
(c) the telephone number must be a multiple of 100?
(d) the first 3 digits are 481?
(e) no repetitions are allowed?
Thanks
This question is from textbook college algebra
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! How many 7-digit telephone numbers are possible if the first digit cannot be 0 and
(a) only odd digits may be used?
9 ways to choose the 1st digit
5^6 ways to choose 6 odd numbers
Total ways = 9*5^6=140625 ways
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(b) the telephone number must be a multiple of 10, (that is, it must end in 0)
9 ways to choose the 1st digit
1 way to choose the 7th digit
5^10 ways to choose the remaining digits
Total ways = 9*10^5=900,000
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(c) the telephone number must be a multiple of 100?
The last two digits must be zero
9 ways to choose the 1st digit.
1 way to choose the 7th and the 6th digit
10^4 ways to choolse the remaining digits
Total ways = 9*10^4=90,000
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(d) the first 3 digits are 481?
1 way to pick the 1st three digits
10^4 ways to pick the other digits
Total 10,000 ways
(e) no repetitions are allowed?
9 ways to pick the 1st digit
9 ways to pick the 2nd
8 ways
7 ways
etc.
Total ways: 9*9!=3265920 ways
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Cheers,
Stan H.
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