Final Position
Initial Position
3.
Supriya remembers the first eight digits of her phone number but she forgot the last
ninth digit of it. She only remembers that the last digit is amongst 1, 2, 3, 5, 6 and 8.
How many possible combinations of numbers can be formed?
A 6
B. 7
C. 8
D. 10
Answers
Answer:
A.6
Step-by-step explanation:
there are 6 possibilities
Answer:
tq for answer my friend
Step-by-step explanation:
Let us consider two cases.
Case 1: The last number is not 9
Let us first construct a 7 digit number without any 9s. There are 9^6 X 4 ways of doing this because of the 9 possible candidates for the first 6 digits and 4 candidates(1,3,5,7) for the last digit. Now, in each of these numbers there are 7 ways of inserting a 9 ie, before first digit, before second digit,.., before last digit.This gives 9^6 X4 X7 combinations. But note that there is still the possibility of choosing 0 as the first digit( which would make the resulting number have <8 digits). To counter these cases we just need to subtract the numbers which have their first digit as 0, have a single 9 and their last digit is odd and not 9. Applying similar arguments as before this gives 9^5 X 4 X 6 combinations. So, there are (9^6 X4 X7)-(9^5*4*6)=9^5 X 228 ways of choosing numbers such that your conditions are satisfied and the last number is not 9.
Case 2: The last number is 9
This is a trivial case because if the last digit is 9, the rest of the 7 digits have 9 possible candidates except for the first digit which has 8 candidates(excluding 9 and 0) and total number of choices is 9^6 X 8.
Therefore, in total your friend has to check for (9^5 X228) + 9^6 X 8= 9^5 X 300 numbers in the worst case where the last number your friend tries turns out to be correct.