The largest 5-digit number having three different digits is:
a.98978
b. 99897
c. 99987
d. 98799

Hint: To solve the above question we first take an assumption that fulfills our requirements given in the question and then if we want largest we should start putting with 9 on higher place values and then 8, 7, 6….so on.

Complete step-by-step answer:
As per the question, we need the largest five-digit number, and that number’s three digits should be different means three can be the same. We assume xyz is a number whose three digits are different that are x, y, and z also three digits are the same that is x.
To fulfill the requirement of the question we will consider the largest five digit number that is 99999. But in this number, all digits are the same that’s why we will consider 9 on only the ten-thousandth place, thousandth and hundredth place of the number because we want the largest number so we will put 9 on higher place values. Now, 8 on the tenth place and 7 on one's place. The number formed is 99987, as we can see this is the largest five-digit number which contains three different digits which are 9, 8, and 7.
Yes, this is the right number and option c is the right option.

Note: We should remember that if we want the smallest number then 0 should be on higher place values and then 1, 2... and so on. If the largest number is required then 9 should be on higher place values and then 8, 7... and so on.