If any seven digits could be used to form a telephone number, how many seven dig
ID: 3141571 • Letter: I
Question
If any seven digits could be used to form a telephone number, how many seven digit telephone numbers would not have repeated digits?How many seven digit telephone numbers would have at least one repeated digit?
If any seven digits could be used to form a telephone number, how many seven digit telephone numbers would not have repeated digits?
How many seven digit telephone numbers would have at least one repeated digit?
How many seven digit telephone numbers would have at least one repeated digit?
Explanation / Answer
If repeatition is not allowed,
First digit cannot be 0 to form 7 digit number.
So first digit can be filled by 9 ways.
Second digit by 9 ways , third by 8 ways , forth by 7 ways , fifth by 6 ways, sixth by 5 wayss, and seventh by 4 ways.
total number of ways = 9 * 9* 8* 7* 6* 5* 4 = 544320.
For at least one repeated digit
If repeatition is allowed total number of ways to form 7 digit number = 9 * 106 = 9000000
So Total number of ways to form seven digit telephone number with at least one repeated digit =
total number with repeatitionis allowed - total number with repeation is not allowed.
= 9000000- 544320 = 8455680.
If 0 could be start first number as question doesn't given any restrictions then answer for above both condtion
would be.
If repeatition is not allowed,
10*9*8*7*6*5*4 = 604800 ways.
For at least one repeated digit
There are total number = 107 = 10000000
For at least one repeated digit = 10000000-604800 = 9395200.