SOLUTION: 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,

Question 115912: 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?
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
a) options are 1,3,5,7,9 thus the choices are: 5^7=78,125 possible combinations.
b) options are 0,1,2,3,4,5,6,7,8,9 for the first 6 digits & only 1 option for the last digit: thus 10^5*1=100,000+1-100,001 possible combinations.
c)options are 0,1,2,3,4,5,6,7,8,9 for the first 5 digits & 1 each for the last 2 digits: thus 10^4*181=10,000+1+1=10,002 possible combinations.
d) 1 choice for the first 3 digits which leaves 10 choices for the next 4 positions or 1+10^4=1+10,000=10,001.
e) 10*9*8*7*6*5*4=604,800 choices.
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