Question

In: Statistics and Probability

The number 52430 is a 5-digit number whereas 03201 is not a 5-digit number. Determine the...

The number 52430 is a 5-digit number whereas 03201 is not a 5-digit number. Determine the
number of 5-digit multiples of 5 that can be created using the digits 0 to 9, if digits may not be
repeated

Solutions

Expert Solution

solution:

Total no.of digits possible(0-9) = 10

Given that constraints for the formation of 5-digit number

----> First digit cannot be zero

----> Digits cannot be repeated

----> Digit must be a multiple of 5 (i.e., last digit must either 0 or 5)

1st digit

2nd digit

3rd digit

4th digit

5th digit

Case-i: When the last digit is 5

1st Digit : Here, The total no.of possible digits = 8 [since 0,5 cannot be used here ]

2nd Digit : The no,of possible digits = 8 [since 1 digit previously and 5 will be used at last ]

3rd digit: Here,The no.of possible digits = 7

4th digit : Here, the no.of possible digits = 6

5th digit:Here,the no.of possible digits = 1 [ i.e., 5]

By Multiplication rule

Total no.of possible 5-digit numbers with last digit 5 = 8*8*7*6*1 = 2688

Case-ii: When the last digit is 0

1st Digit : Here, The total no.of possible digits = 9 [since 0 cannot be used here ]

2nd Digit : The no,of possible digits = 8 [since 1 digit previously and 0 will be used at last ]

3rd digit: Here,The no.of possible digits = 7

4th digit : Here, the no.of possible digits = 6

5th digit:Here,the no.of possible digits = 1 [ i.e., 0]

By Multiplication rule

Total no.of possible 5-digit numbers with last digit 0 = 9*8*7*6*1 = 3024

The total number of 5-digit multiples of 5 that can be created using 0 to 9 = 2688+3024 = 5712

orchestra answered 1 year ago

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