How many three-digit numbers that are divisible by 5, can be formed, using the digits 0,2,3,5,7,

step 1 7 and it reads that how many 3 digit numbers that are divisible by 5 can be formed using digit 0

How many three-digit numbers that are divisible by 5, can be...

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Counting with Restrictions

This concept focuses on counting methods in combinatorics when there are constraints on how selections can be made. Problems of this nature involve additional conditions such as a restriction on using each digit only once and positional restrictions (such as the hundreds digit cannot be 0 in a three-digit number). The restrictions require careful case-by-case analysis to ensure that all conditions are met while counting the total valid arrangements.

Permutations

Permutations refer to the arrangement of objects in a specific order. In this context, it involves arranging available digits (without repetition) to form numbers. The ordering is significant because even a change in the position of a digit can create a different number, and specific constraints (like the fixed unit digit for divisibility purposes) influence the total count.

Divisibility Rules

This concept involves understanding the criteria that determine whether a number is divisible by a specific divisor—in this case, 5. For divisibility by 5, the rule requires that the unit (ones) digit of the number must be either 0 or 5. This rule is critically used in problems where numbers must meet divisibility conditions by fixing certain digit positions.

Transcript

Please give Ace some feedback