If a 4 digit number greater than 5000 is to be formed with the digits 0,1,3,5,6,7, what is the probability - Maths - Probability

Question

If a 4 digit number greater than 5000 is to be formed with the
digits 0,1,3,5,6,7, what is the probability that it will be
divisible by 5 when the repetition of digits is not allowed?

Suraj Basappa Belure · Accepted Answer

Dear Student,
Please find below the solution to the asked query:

We have:0,1,3,5,7 i Digits can be repeated
First digit can be filled by only 5 and 7 as number should be greater than 5000
Last digit can be filled with 0 or 5 only as number should be divisible by 5
Rest two digits can be filled by any of 5 digits i
e  0,1,3,5,7
Hence2 ×  5× 5 × 2 =100 Answerii Digits can be repeated
Casea When number starts with 5
When number starts with 5, then last digit can be filled with 0 only
Second digit can be filled with 3 options 1,3,7 and third digits can befilled with remaining two options
Hence1 × 3 × 2 × 1 =6Caseb When number does starts with 7When number does starts with 7, then last digit can be filled with 0 or 5
1 × 3 × 2 × 2 =12Hence total numbers=6+12=18 Answer

Regards

If a 4 digit number greater than 5000 is to be formed with the digits 0,1,3,5,6,7, what is the probability that it will be divisible by 5 when the repetition of digits is not allowed?