SOLUTION: Assume a telephone number consists of 8 digits, and the first and last digits cannot be 0.
(a) If repetitions are allowed, how many telephone numbers are possible if
(i) there is
Algebra.Com
Question 406031: Assume a telephone number consists of 8 digits, and the first and last digits cannot be 0.
(a) If repetitions are allowed, how many telephone numbers are possible if
(i) there is no restriction;
(ii) they are odd and start with 2?
(b) If repetitions are not allowed, how many telephone numbers are possible if
(i) there is no restriction;
(ii) they are divisible by 3 and the first digit is less than 5.
Answer by sudhanshu_kmr(1152) (Show Source): You can put this solution on YOUR website!
A) (i) for first and last position any digit except 0, for other any of 10 digits
total no. of possible numbers = 9*10*10*10*10*10*10*9 = 81000000 = 81*10^6
(ii)
for odd numbers odd number must in at unit place....
total no. of odd numbers = 5
we can put digit 2 at first place by 1 way.
total no. of possible numbers = 1*10*10*10*10*10*10*5 = 5000000 = 5 * 10^6
B) if repetitions are not allowed...
(i) as first place and last can't be zero,
no. of ways to put digit at first and last position = 9*8 = 72
( now we have 8 digits and 6 positions to fill )
no. of ways to put digit at remaining 6 positions = 8P6 = 20160
total no. of ways = 72*20160 = 1451520
RELATED QUESTIONS
How many 7-digit telephone numbers are possible if the first digit cannot be 0 and
(a) (answered by checkley71)
How many four digits number can be formed with the 10 digits 0-9
a) If repetitions are... (answered by ikleyn)
Can you please help me with this problem?
How many 7-digit telephone numbers are... (answered by stanbon)
ow many 7-digit telephone numbers are possible if the first digit cannot be six and... (answered by Boreal)
Principles of Counting or Permutations. What formula do I use here.
Telephone... (answered by palanisamy)
1.how many 7-digit telephone numbers are possible if the first digit cannot be 0 and
a:... (answered by 1433)
how many 4-digit numbers can be formed with the 10 digits 0,1,2,3...9 of (a)repetitions... (answered by Edwin McCravy)
How many four-digit numbers can be formed from the digits 0,1,2,3,4,5 if no repetitions... (answered by kev82)
A) A college wants to create an easily accessible 7-digit telephone to be used for... (answered by stanbon)