a bank has 6 digit account number with no reputation of digit within account number the first and last digit of the account number is fixed tob 4 and 7 how many such account number are possible?
Answers
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Correct Question
A bank has 6 digit account number with no repetition of digits within the account number. The first and last digit of the account number is fixed to be 4 and 7. How many such account numbers are possible?
Answer
1680 such account numbers are possible.
Given
- A bank has 6 digit account number with no repetition of digits.
- The first and last digit of the account number is fixed to be 4 and 7.
To Find
The number of account numbers possible
Solution
There are 10 digits in our number system they are
0, 1, 2, 3, ..... 9
Therefore, the 6 numbers for the code will be selected among these 10 digits.
Let the code be represented by _ _ _ _ _ _
According to the problem,
the first and the last digit is fixed to be 4 and 7 respectively. Hence it will look like
4 _ _ _ _ 7
Since we cannot repeat numbers,
we can decide on the second digit in
10 - 2 = 8 ways.
Since we have used up one more digit, now we can decide on the third number in
8 - 1 = 7 ways
Similarly, the fourth number can be decided in
7 - 1 = 6 ways
And lastly, the fifth number can be decided in
6 - 1 = 5 ways.
Therefore, the total number of account numbers possible is
8 X 7 X 6 X 5 ways
= 1680 ways
1680 such account numbers are possible.
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