If 4 - digit numbers greater than 5000 are randomly formed from the digits 0, 1, 3, 5, and 7, what is the probability of the forming a number divisible by 5 when (a) repetition is not allowed (b) repetition is allowed
Answers
Answer:
Step-by-step explanation:
Answer:
a) 33/83
b) 1/4
Explanation:
a) If the digits can be repeated:
The first digit has to be 5or7 to have a number greater than 5000
The number of possible numbers is: 2×5×5×5=250
(2 choices for the first digit and 5 choices for each of the remaining 3 place holders)
(However this includes the number 5000 which is not greater than 5000, so there are 249 possible numbers.
Of these, we want the number to be divisible by 5, so the last digit has to be a 5or0
There are 2×5×5×2=100 possible multiples of 5.
(Remember to exclude the number 5000, so there are 99)
P(divisible by 5)=99/249=33/83
b) If the digits may not be repeated.
This means that once a digit has been chosen, there is one digit less for the choice of the next digit.
The number of possible numbers: 2×4×3×2=48
(The possibility of 5000 does not exist this time because 0 can only be used once.)
Of these, we want the number to be divisible by 5, so the last digit has to be a 5or0
The 5 can be either first or last, but not both.
If the first digit is 5, then the last digit must be 0
5??0
Number of multiples of 5: 1×3×2×1=6
If the last digit is 5 we will have:
7??5
Number of multiples of 5: 1×3×2×1=6
Therefore there are 6+6=12 possible multiples of 5
P(divisible by 5)=12/48=1/4