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
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