Question 170668: : 1.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 0f 10
c: the telephone number must be a multiple of 100
d: the 1st 3 digits are 481
e: no repetition are allowed.This question is from textbook
: 1.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 0f 10
c: the telephone number must be a multiple of 100
d: the 1st 3 digits are 481
e: no repetition are allowed.
Answer by EMStelley(208)   (Show Source):
You can put this solution on YOUR website! I will help you think about a couple of these, but I will certainly not answer them all for you. So we are thinking about a number of the form
XXXXXXX, where the first digits cannot be 0.
For a), only odd digits may be used. How many odd digits are between 0 and 9? 1,3,5,7,9, so there are 5. That means for every digit except the first one, there are 5 choices. So if you fill in the blank with how many choices there are, you have your answer
1,5,5,5,5,5,5. Multiplying, we get that there are 5^6=15625 possible phone numbers.
Part b) is similar, but since the telephone number must be a multiple of 10, that means that the last digit must be 0. So here we have the restrictions of the first and last digit being 0, but all the rest can be anything between 0 and 9 (10 digits). So here we have 10^5=100,000 possibilities (5 places each with 10 possibilities).
|
|
|
