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If a 4 digit number > 5000 are randomly formed from digits 0,1,3,5,7. Find probability of forming a number divisible by 5 when (1) digits are repeated 2) digits are not repeated.

If a 4 digit number > 5000 are randomly formed from digits 0,1,3,5,7. Find probability of forming
a number divisible by 5 when (1) digits are repeated 2) digits are not repeated.

Grade:Upto college level

2 Answers

Latika Leekha
askIITians Faculty 165 Points
7 years ago
A 4 digit number greater than 5000 is randomly formed from digits 0,1,3,5,7.
(1) Repetition is allowed:
We need to form a number greater than 5000, hence, the leftmost digit can be either 5 or 7.
Since, repetition of digits is allowed, so the remaining three places can be filled by 0, 1, 3, 5, or 7.
Hence, the total number of 4 digit numbers that can be formed greater than 5000 are = 2.5.5.5 = 250
But, we can’t count 5000 so the total number becomes 250 – 1 = 249.
The number is divisible by 5 only if the numnber at unit’s place is either 0 or 5.
Hence, the total number of numbers greater than 5000 and divisible by 5 are = 2.5.5.2 – 1 = 99
Hence, the required probability is given by = 99/249
= 33/83.
(2) If repetition of digits is not allowed:
For a number to be greter than 5000, the digit at thousand’s place can be either 5 or 7.
The remaining three places can be filled by any of the four digits.
hence, total number of numbers greater than 5000 = 2.4.3.2 = 48.
When the digit at thousand’s place is 5, units digit can be 0 and the tens and hundreds digit can be any two of the remaining three digits.
Hence, the number of 4 digit numbers starting with 5 and divisible by 5 = 3.2 = 6
When the digit at thousand’s place is 7, units digit can be filled in two ways (0 or 5) and the tens and hundreds digit can be any two of the remaining three digits.
Hence, the number of 4 digit numbers starting with 7 and divisible by 5 = 1.2.3.2 = 12.
therefore, the number of 4 digit numbers greater than 5000 and divisible by 5 = 12 + 6 = 18
hence, the required probability = 18/48 = 3/8.
Thansk & Regards
Latika Leekha
askIITians Faculty
Kushagra Madhukar
askIITians Faculty 629 Points
one year ago
Dear student,
Please find the attached solution to problem.
 
A 4 digit number greater than 5000 is randomly formed from digits 0,1,3,5,7.
(1) Repetition is allowed:
We need to form a number greater than 5000, hence, the leftmost digit can be either 5 or 7.
Since, repetition of digits is allowed, so the remaining three places can be filled by 0, 1, 3, 5, or 7.
Hence, the total number of 4 digit numbers that can be formed greater than 5000 are = 2.5.5.5 = 250
But, we can’t count 5000 so the total number becomes 250 – 1 = 249.
The number is divisible by 5 only if the numnber at unit’s place is either 0 or 5.
Hence, the total number of numbers greater than 5000 and divisible by 5 are = 2.5.5.2 – 1 = 99
Hence, the required probability is given by = 99/249
= 33/83.
(2) If repetition of digits is not allowed:
For a number to be greter than 5000, the digit at thousand’s place can be either 5 or 7.
The remaining three places can be filled by any of the four digits.
hence, total number of numbers greater than 5000 = 2.4.3.2 = 48.
When the digit at thousand’s place is 5, units digit can be 0 and the tens and hundreds digit can be any two of the remaining three digits.
Hence, the number of 4 digit numbers starting with 5 and divisible by 5 = 3.2 = 6
When the digit at thousand’s place is 7, units digit can be filled in two ways (0 or 5) and the tens and hundreds digit can be any two of the remaining three digits.
Hence, the number of 4 digit numbers starting with 7 and divisible by 5 = 1.2.3.2 = 12.
therefore, the number of 4 digit numbers greater than 5000 and divisible by 5 = 12 + 6 = 18
hence, the required probability = 18/48 = 3/8.
 
Thanks & Regards
Kushagra

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